메뉴 건너뛰기




Volumn 17, Issue 3-4, 2007, Pages 409-493

A conceptual construction of Complexity Levels Theory in spacetime Categorical Ontology: Non-abelian algebraic topology, many-valued logics and dynamic systems

Author keywords

Categorical ontology and the theory of levels; Formal foundation and relational structure of categorical ontology and emergent complexity theories; Ontological essence and Universal properties of items

Indexed keywords


EID: 37649005768     PISSN: 11221151     EISSN: 15728390     Source Type: Journal    
DOI: 10.1007/s10516-007-9010-3     Document Type: Article
Times cited : (10)

References (179)
  • 1
    • 0036749184 scopus 로고    scopus 로고
    • Multiple categories: The equivalence of a globular and cubical approach
    • Al-Agl FA, Brown R, Steiner R (2002) Multiple categories: the equivalence of a globular and cubical approach. Adv in Math 170:711-718
    • (2002) Adv Math , vol.170 , pp. 711-718
    • Al-Agl, F.A.1    Brown, R.2    Steiner, R.3
  • 3
    • 5344276756 scopus 로고
    • The geometric phase
    • Anandan J (1992) The geometric phase. Nature 360:307-313
    • (1992) Nature , vol.360 , pp. 307-313
    • Anandan, J.1
  • 4
    • 0038771012 scopus 로고
    • The holonomy groupoid of a locally topological groupoid
    • Aof ME, Brown R (1992) The holonomy groupoid of a locally topological groupoid. Top Appl 47:97-113
    • (1992) Top Appl , vol.47 , pp. 97-113
    • Aof, M.E.1    Brown, R.2
  • 6
    • 17044391847 scopus 로고    scopus 로고
    • Higher dimensional algebra and Planck scale physics
    • Callender C, Hugget N (eds) Cambridge University Press
    • Baez J (2001) Higher dimensional algebra and Planck scale physics. In: Callender C, Hugget N (eds) Physics meets philosophy at the Planck scale. Cambridge University Press, pp 177-195
    • (2001) Physics Meets Philosophy at the Planck Scale , pp. 177-195
    • Baez, J.1
  • 7
    • 36449001406 scopus 로고
    • Higher dimensional algebra and topological quantum field theory
    • Baez J, Dolan J (1995) Higher dimensional algebra and topological quantum field theory. J Math Phys 36:6073-6105
    • (1995) J Math Phys , vol.36 , pp. 6073-6105
    • Baez, J.1    Dolan, J.2
  • 8
    • 33748867278 scopus 로고
    • Organismic supercategories: Towards a unitary theory of systems
    • Baianu IC, Marinescu M (1968) Organismic supercategories: towards a unitary theory of systems. Bull Math Biophys 30:148-159
    • (1968) Bull Math Biophys , vol.30 , pp. 148-159
    • Baianu, I.C.1    Marinescu, M.2
  • 9
    • 0014925242 scopus 로고
    • Organismic supercategories: II. on multistable systems
    • Baianu IC (1970) Organismic supercategories: II. On multistable systems. Bull Math Biophys 32:539-561
    • (1970) Bull Math Biophys , vol.32 , pp. 539-561
    • Baianu, I.C.1
  • 10
    • 0015119119 scopus 로고
    • Organismic supercategories and qualitative dynamics of systems
    • 3
    • Baianu IC (1971a) Organismic Supercategories and qualitative dynamics of systems. Bull Math Biophys 33(3):339-354
    • (1971) Bull Math Biophys , vol.33 , pp. 339-354
    • Baianu, I.C.1
  • 13
    • 0015815439 scopus 로고
    • Some algebraic properties of (M,R)-systems
    • Baianu IC (1973) Some algebraic properties of (M,R)-systems. Bull Math Biophys 35:213-217
    • (1973) Bull Math Biophys , vol.35 , pp. 213-217
    • Baianu, I.C.1
  • 15
    • 0017576272 scopus 로고
    • A logical model of genetic activities in Łukasiewicz algebras: The non-linear theory
    • Baianu IC (1977) A logical model of genetic activities in Łukasiewicz algebras: the non-linear theory. Bull Math Biology 39:249-258
    • (1977) Bull Math Biology , vol.39 , pp. 249-258
    • Baianu, I.C.1
  • 16
    • 0018869940 scopus 로고
    • Natural transformations of organismic structures
    • Baianu IC (1980a) Natural transformations of organismic structures. Bull Math Biophys 42:431-446
    • (1980) Bull Math Biophys , vol.42 , pp. 431-446
    • Baianu, I.C.1
  • 17
    • 37649022057 scopus 로고
    • On partial order and disorder in biological systems. Letter to the Editor
    • Baianu IC (1980b) On partial order and disorder in biological systems. Letter to the Editor Bull Math Biophys 42:601-605
    • (1980) Bull Math Biophys , vol.42 , pp. 601-605
    • Baianu, I.C.1
  • 18
    • 33748879068 scopus 로고
    • Natural transformation models in molecular biology
    • Denver, CO.; Eprint, http://cogprints.org/3675/0l/Naturaltransfmolbionu6. pdf
    • Baianu IC (1983) Natural transformation models in molecular biology. In: Proceedings of the SIAM Natl. Meet., Denver, CO.; Eprint: http://www.cogprints. org/3675/ http://cogprints.org/3675/0l/Naturaltransfmolbionu6.pdf
    • (1983) Proceedings of the SIAM Natl. Meet.
    • Baianu, I.C.1
  • 19
    • 33748867649 scopus 로고
    • A molecular-set-variable model of structural and regulatory activities in metabolic and genetic networks
    • Baianu IC (1984) A molecular-set-variable model of structural and regulatory activities in metabolic and genetic networks. FASEB Proc 43:917
    • (1984) FASEB Proc , vol.43 , pp. 917
    • Baianu, I.C.1
  • 20
    • 33748822184 scopus 로고
    • Computer models and automata theory in biology and medicine
    • Witten M (ed) Pergamon Press, New York, pp 1513-1577; CERN Preprint No. EXT-2004-072
    • Baianu IC (1987a) Computer models and automata theory in biology and medicine. In: Witten M (ed) Mathematical models in medicine, vol 7. Pergamon Press, New York, pp 1513-1577; CERN Preprint No. EXT-2004-072: http://doe.cern.ch//archive/electronic/other/ext/ext-2004-072.pdf
    • (1987) Mathematical Models in Medicine , vol.7
    • Baianu, I.C.1
  • 21
    • 37648999291 scopus 로고
    • Proceed. relational biology symp. Argentina; CERN Preprint No.EXT-2004-067
    • Baianu IC (1987b) Molecular models of genetic and organismic structures. In: Proceed. relational biology symp. Argentina; CERN Preprint No.EXT-2004-067 http://doc.cern.ch/archive/electronic/other/ext/ext-2004-0-67/ MolecularModels-ICB3.doc
    • (1987) Molecular Models of Genetic and Organismic Structures
    • Baianu, I.C.1
  • 23
    • 37649024776 scopus 로고    scopus 로고
    • Quantum Interactomics In: Cancer-Sept13k4E-cuteprt.pdf, Preprint No. 00001978 http://bioline.utsc.utoronto.ca/archive/00001978/
    • Baianu IC (2004b) Quantum interactomics and cancer mechanisms, Preprint No. 00001978 - http://www.bioline.utsc.utoronto.ca/archive/00001978/01/ Quantum Interactomics In: Cancer-Sept13k4E-cuteprt.pdf http://bioline.utsc.utoronto.ca/ archive/00001978/
    • (2004) Quantum Interactomics and Cancer Mechanisms
    • Baianu, I.C.1
  • 24
    • 33748846802 scopus 로고    scopus 로고
    • Robert Rosen's work and complex systems biology
    • 1-2
    • Baianu IC (2006) Robert Rosen's work and complex systems biology. Axiomathes 16(1-2):25-34
    • (2006) Axiomathes , vol.16 , pp. 25-34
    • Baianu, I.C.1
  • 28
    • 33748849324 scopus 로고    scopus 로고
    • Complex nonlinear biodynamics in categories, higher dimensional algebra and Łukasiewicz-Moisil topos: Transformations of neuronal, genetic and neoplastic networks
    • 1-2
    • Baianu IC, Brown R, Georgescu G, Glazebrook JF (2006) Complex nonlinear biodynamics in categories, higher dimensional algebra and Łukasiewicz- Moisil Topos: transformations of neuronal, genetic and neoplastic networks. Axiomathes 16(1-2):65-122
    • (2006) Axiomathes , vol.16 , pp. 65-122
    • Baianu, I.C.1    Brown, R.2    Georgescu, G.3    Glazebrook, J.F.4
  • 30
    • 37649022166 scopus 로고    scopus 로고
    • Categorical ontology of complex spacetime structures: The emergence of life and human consciousness
    • this issue
    • Baianu IC, Brown R, Glazebrook JF (2007b) Categorical ontology of complex spacetime structures: the emergence of life and human consciousness. Axiomathes 17 (this issue)
    • (2007) Axiomathes , vol.17
    • Baianu, I.C.1    Brown, R.2    Glazebrook, J.F.3
  • 31
    • 37649016282 scopus 로고    scopus 로고
    • A non-abelian categorical ontology of spacetime and quantum gravity
    • this issue
    • Baianu IC, Brown R, Glazebrook JF (2007c) A non-abelian categorical ontology of spacetime and quantum gravity. Axiomathes 17 (this issue)
    • (2007) Axiomathes , vol.17
    • Baianu, I.C.1    Brown, R.2    Glazebrook, J.F.3
  • 32
    • 37649014788 scopus 로고    scopus 로고
    • From simple to super- and ultra-complex systems: Towards a non-abelian dynamics paradigm shift
    • Poli R et al (eds) Springer, Berlin (in press)
    • Baianu IC, Poli R (2008) From simple to super- and ultra-complex systems: towards a non-abelian dynamics paradigm shift. In: Poli R et al (eds) Theory and applications of ontology, vol 1. Springer, Berlin (in press)
    • (2008) Theory and Applications of Ontology , vol.1
    • Baianu, I.C.1    Poli, R.2
  • 34
    • 37649001504 scopus 로고
    • The wide-sense kinetics of molecular sets
    • Bartholomay A (1971) The wide-sense kinetics of molecular sets. Bull Math Biophys 33(3):326-328
    • (1971) Bull Math Biophys , vol.33 , Issue.3 , pp. 326-328
    • Bartholomay, A.1
  • 35
    • 0000194417 scopus 로고
    • The logic of quantum mechanics
    • Birkhoff G, von Neumann J (1936) The logic of quantum mechanics. Ann Math 37:823-843
    • (1936) Ann Math , vol.37 , pp. 823-843
    • Birkhoff, G.1    Von Neumann, J.2
  • 37
    • 84963109351 scopus 로고
    • Groupoids and Van Kampen's theorem
    • 3
    • Brown R (1967) Groupoids and Van Kampen's theorem. Proc London Math Soc 17(3):385-401
    • (1967) Proc London Math Soc , vol.17 , pp. 385-401
    • Brown, R.1
  • 38
    • 0002354714 scopus 로고
    • From groups to groupoids: A brief survey
    • Brown R (1987) From groups to groupoids: a brief survey. Bull London Math Soc 19:113-134
    • (1987) Bull London Math Soc , vol.19 , pp. 113-134
    • Brown, R.1
  • 39
    • 0000483988 scopus 로고    scopus 로고
    • Homotopy theory, and change of base for groupoids and multiple groupoids
    • Brown R (1996) Homotopy theory, and change of base for groupoids and multiple groupoids. Appl Categorical Struct 4:175-193
    • (1996) Appl Categorical Struct , vol.4 , pp. 175-193
    • Brown, R.1
  • 43
    • 0037918950 scopus 로고    scopus 로고
    • Lie local subgroupoids and their holonomy and monodromy Lie groupoids
    • Brown R, Içen I (2001) Lie local subgroupoids and their holonomy and monodromy Lie groupoids. Top Appl 115:125-138
    • (2001) Top Appl , vol.115 , pp. 125-138
    • Brown, R.1    Içen, I.2
  • 44
    • 0031558122 scopus 로고    scopus 로고
    • Van Kampen theorems for categories of covering morphisms in lextensive categories
    • Brown R, Janelidze G (1997) Van Kampen theorems for categories of covering morphisms in lextensive categories. J Pure Appl Algebra 119:255-263
    • (1997) J Pure Applied Algebra , vol.119 , pp. 255-263
    • Brown, R.1    Janelidze, G.2
  • 45
    • 1342303392 scopus 로고    scopus 로고
    • Galois theory and a new homotopy double groupoid of a map of spaces
    • Brown R, Janelidze G (2004) Galois theory and a new homotopy double groupoid of a map of spaces. Appl Categorical Struct 12:63-80
    • (2004) Appl Categorical Struct , vol.12 , pp. 63-80
    • Brown, R.1    Janelidze, G.2
  • 46
    • 0001301955 scopus 로고
    • Van Kampen Theorems for diagrams of spaces
    • Brown R, Loday J-L (1987) Van Kampen Theorems for diagrams of spaces. Topology 26:311-337
    • (1987) Topology , vol.26 , pp. 311-337
    • Brown, R.1    Loday, J.-L.2
  • 47
    • 45749090130 scopus 로고    scopus 로고
    • in preparation http://www.bangor.ac.uk/mas010/nonab-t/partI010604.pdf
    • Brown R, Higgins PJ, Sivera R (2008) Non-Abelian algebraic topology, in preparation. http://www.bangor.ac.uk/mas010/nonab-a-t.html ; http://www.bangor.ac.uk/mas010/nonab-t/partI010604.pdf
    • (2008) Non-Abelian Algebraic Topology
    • Brown, R.1    Higgins, P.J.2    Sivera, R.3
  • 48
    • 33748864326 scopus 로고    scopus 로고
    • Categorical language and hierarchical models for cell systems
    • Paton R, Bolouri H, Holcombe M, Parish JH, Tateson R (eds) Natural Computing Series. Springer Verlag
    • Brown R, Paton R, Porter T (2004) Categorical language and hierarchical models for cell systems. In: Paton R, Bolouri H, Holcombe M, Parish JH, Tateson R (eds) Computation in cells and tissues-perspectives and tools of thought. Natural Computing Series. Springer Verlag, pp 289-303
    • (2004) Computation in Cells and Tissues-perspectives and Tools of Thought , pp. 289-303
    • Brown, R.1    Paton, R.2    Porter, T.3
  • 49
    • 33748875567 scopus 로고    scopus 로고
    • Category theory and higher dimensional algebra: Potential descriptive tools in neuroscience
    • Singh N (ed) Proceedings of the international conference on theoretical neurobiology, Delhi, February 2003, National Brain Research Centre
    • Brown R, Porter T (2003) Category theory and higher dimensional algebra: potential descriptive tools in neuroscience. In: Singh N (ed) Proceedings of the international conference on theoretical neurobiology, Delhi, February 2003, National Brain Research Centre, Conference Proceedings, vol 1, pp 80-92
    • (2003) Conference Proceedings , vol.1 , pp. 80-92
    • Brown, R.1    Porter, T.2
  • 50
    • 0042428783 scopus 로고    scopus 로고
    • Towards a 2-dimensional notion of holonomy
    • Brown R., Içen I (2003) Towards a 2-dimensional notion of holonomy. Adv Math 178:141-175
    • (2003) Adv Math , vol.178 , pp. 141-175
    • Brown, R.1    Içen, I.2
  • 52
    • 84981434101 scopus 로고
    • Topological groupoids I: Universal constructions
    • Brown R, Hardy JPL (1976) Topological groupoids I: universal constructions. Math Nachr 71:273-286
    • (1976) Math Nachr , vol.71 , pp. 273-286
    • Brown, R.1    Hardy, J.P.L.2
  • 53
    • 0000960526 scopus 로고
    • The monodromy groupoid of a Lie groupoid
    • Brown R, Mucuk O (1995) The monodromy groupoid of a Lie groupoid. Cah Top Géom Diff Cat 36:345-369
    • (1995) Cah Top Géom Diff Cat , vol.36 , pp. 345-369
    • Brown, R.1    Mucuk, O.2
  • 54
    • 0002706577 scopus 로고    scopus 로고
    • Foliations, locally Lie groupoids, and holonomy
    • Brown R, Mucuk O (1996) Foliations, locally Lie groupoids, and holonomy. Cah Top Géom Diff Cat 37:61-71
    • (1996) Cah Top Géom Diff Cat , vol.37 , pp. 61-71
    • Brown, R.1    Mucuk, O.2
  • 56
    • 0000739465 scopus 로고
    • Double groupoids and crossed modules
    • Brown R, Spencer CB (1976) Double groupoids and crossed modules. Cah Top Géom Diff 17:343-362
    • (1976) Cah Top Géom Diff , vol.17 , pp. 343-362
    • Brown, R.1    Spencer, C.B.2
  • 57
    • 3543069108 scopus 로고    scopus 로고
    • Free crossed resolutions of groups and presentations of modules of identities among relations
    • Brown R, Razak Salleh A (1999) Free crossed resolutions of groups and presentations of modules of identities among relations. LMS J Comput Math 2:25-61
    • (1999) LMS J Comput Math , vol.2 , pp. 25-61
    • Brown, R.1    Razak Salleh, A.2
  • 59
    • 0242511144 scopus 로고    scopus 로고
    • Van Kampen theorems for toposes
    • Bunge M, Lack S (2003) Van Kampen theorems for toposes. Adv Math 179:291-317
    • (2003) Adv Math , vol.179 , pp. 291-317
    • Bunge, M.1    Lack, S.2
  • 60
    • 0000922234 scopus 로고    scopus 로고
    • Spacetime and the philosophical challenges of quantum gravity
    • Callender C, Hugget N (eds) Cambridge University Press
    • Butterfield J, Isham CJ (2001) Spacetime and the philosophical challenges of quantum gravity. In: Callender C, Hugget N (eds) Physics meets philosophy at the Planck scale. Cambridge University Press, pp 33-89
    • (2001) Physics Meets Philosophy at the Planck Scale , pp. 33-89
    • Butterfield, J.1    Isham, C.J.2
  • 61
    • 0038855384 scopus 로고    scopus 로고
    • A topos perspective on the Kochen-Specker theorem I-IV
    • 1999, 2000
    • Butterfield J, Isham CJ 1998, 1999, 2000-2002, A topos perspective on the Kochen-Specker theorem I-IV, Int J Theor Phys 37(11):2669-2733.
    • (1998) Int J Theor Phys , vol.37 , Issue.11 , pp. 2669-2733
    • Butterfield, J.1    Isham, C.J.2
  • 66
    • 37649014040 scopus 로고
    • Abstract representations of biological systems in organismic supercategories: II. Limits and colimits
    • Comoroshan S, Baianu IC (1969) Abstract representations of biological systems in organismic supercategories: II. Limits and colimits. Bull Math Biophys 31:84
    • (1969) Bull Math Biophys , vol.31 , pp. 84
    • Comoroshan, S.1    Baianu, I.C.2
  • 69
    • 84972495953 scopus 로고
    • On the van Kampen theorem
    • Crowell RH (1959) On the van Kampen theorem. Pacific J Math 9:43-50
    • (1959) Pacific J Math , vol.9 , pp. 43-50
    • Crowell, R.H.1
  • 72
    • 0001116464 scopus 로고
    • Homologie nicht-additive Funktoren. Anwendungen
    • Dold A, Puppe D (1961) Homologie nicht-additive Funktoren. Anwendungen. Ann Inst Fourier Grenoble 11:201-312
    • (1961) Ann Inst Fourier Grenoble , vol.11 , pp. 201-312
    • Dold, A.1    Puppe, D.2
  • 74
    • 21844465206 scopus 로고
    • Globalizing fibrations by schedules
    • Dyer E, Eilenberg S (1988) Globalizing fibrations by schedules. Fund Math 130:125-136
    • (1988) Fund Math , vol.130 , pp. 125-136
    • Dyer, E.1    Eilenberg, S.2
  • 77
    • 0041905631 scopus 로고
    • Structures locales et structures infinitésimales
    • Ehresmann C (1952) Structures locales et structures infinité simales. C.R.A.S. Paris 274:587-589
    • (1952) C.R.A.S. Paris , vol.274 , pp. 587-589
    • Ehresmann, C.1
  • 78
    • 0004363544 scopus 로고
    • Catégories topologiques et catégories diffé rentiables
    • Ehresmann C (1959) Catégories topologiques et catégories différentiables. Coll Géom Diff Glob Bruxelles pp 137-150
    • (1959) Coll Géom Diff Glob Bruxelles , pp. 137-150
    • Ehresmann, C.1
  • 79
    • 37649003072 scopus 로고
    • Catégories doubles des quintettes: Applications covariantes
    • Ehresmann C (1963) Catégories doubles des quintettes: applications covariantes. CRAS Paris 256:1891-1894
    • (1963) CRAS Paris , vol.256 , pp. 1891-1894
    • Ehresmann, C.1
  • 81
    • 0023085396 scopus 로고
    • Hierarchical evolutive systems: A mathematical model for complex systems
    • 1
    • Ehresmann AC, Vanbremeersch J-P (1987) Hierarchical evolutive systems: a mathematical model for complex systems. Bull Math Biol 49(1):13-50
    • (1987) Bull Math Biol , vol.49 , pp. 13-50
    • Ehresmann, A.C.1    Vanbremeersch, J.-P.2
  • 82
    • 33748851569 scopus 로고    scopus 로고
    • The memory evolutive systems as a model of Rosen's organisms
    • (1-2
    • Ehresmann AC, Vanbremeersch J-P (2006) The memory evolutive systems as a model of Rosen's organisms. Axiomathes 16 (1-2):13-50
    • (2006) Axiomathes , vol.16 , pp. 13-50
    • Ehresmann, A.C.1    Vanbremeersch, J.-P.2
  • 85
    • 37649008055 scopus 로고
    • Natural isomorphisms in group theory
    • Eilenberg S, MacLane S (1942) Natural isomorphisms in group theory. Am Math Soc 43:757-831
    • (1942) Am Math Soc , vol.43 , pp. 757-831
    • Eilenberg, S.1
  • 86
    • 84968491262 scopus 로고
    • The general theory of natural equivalences
    • Eilenberg S, MacLane S (1945) The general theory of natural equivalences. Trans Am Math Soc 58:231-294
    • (1945) Trans Am Math Soc , vol.58 , pp. 231-294
    • Eilenberg, S.1
  • 87
    • 0007414472 scopus 로고
    • A form of logic suited for biology
    • Rosen R.(ed) Academic Press New York
    • Elsasser MW (1981) A form of logic suited for biology. In: Rosen R (ed) Progress in theoretical biology, vol 6. Academic Press, New York, pp 23-62
    • (1981) Progress in Theoretical Biology , vol.6 , pp. 23-62
    • Elsasser, M.W.1
  • 88
    • 0004199048 scopus 로고    scopus 로고
    • Abelian categories
    • formerly published by Harper and Row, New York, 1964
    • Freyd P (2003) Abelian categories. Repr Theory Appl Categ 3:1-190 (formerly published by Harper and Row, New York, 1964)
    • (2003) Repr Theory Appl Categ , vol.3 , pp. 1-190
    • Freyd, P.1
  • 89
    • 0001216833 scopus 로고
    • Des catégories abéliennes
    • Gabriel P (1962) Des catégories abéliennes. Bull Soc Math France 90:323-448
    • (1962) Bull Soc Math France , vol.90 , pp. 323-448
    • Gabriel, P.1
  • 91
    • 33748869559 scopus 로고    scopus 로고
    • N-valued Logics and Łukasiewicz-Moisil algebras
    • 1-2
    • Georgescu G (2006) N-valued Logics and Łukasiewicz-Moisil Algebras. Axiomathes 16(1-2):123-136
    • (2006) Axiomathes , vol.16 , pp. 123-136
    • Georgescu, G.1
  • 92
    • 22144451802 scopus 로고
    • On the characterization of Łukasiewicz-Moisil algebras
    • 4
    • Georgescu G, Vraciu C (1970) On the characterization of Łukasiewicz-Moisil algebras. J Algebra 16(4):486-495
    • (1970) J Algebra , vol.16 , pp. 486-495
    • Georgescu, G.1    Vraciu, C.2
  • 93
    • 33744777430 scopus 로고    scopus 로고
    • Nonlinear dynamics of networks: The groupoid formalism
    • 3
    • Golubitsky M, Stewart I (2006) Nonlinear dynamics of networks: the groupoid formalism. Bull Am Math Soc 43(3):305-364
    • (2006) Bull Am Math Soc , vol.43 , pp. 305-364
    • Golubitsky, M.1    Stewart, I.2
  • 95
    • 1342297962 scopus 로고    scopus 로고
    • Some geometric perspectives in concurrency theory
    • 2
    • Goubault E (2003) Some geometric perspectives in concurrency theory. Homology, Homotopy Appl 5(2):95-136
    • (2003) Homology, Homotopy Appl , vol.5 , pp. 95-136
    • Goubault, E.1
  • 97
    • 84972570012 scopus 로고
    • Sur quelques points d'algèbre homologique
    • 2
    • Grothendieck A (1957) Sur quelques points d'algèbre homologique. Tǒhoku Math J 9(2):119-221
    • (1957) Tǒhoku Math J , vol.9 , pp. 119-221
    • Grothendieck, A.1
  • 99
    • 0003803207 scopus 로고
    • Revêtements étales et Groupe Fondamental (SGA1), chapter VI: Catégories fibrées et descente
    • Springer-Verlag, Berlin
    • Grothendieck A (1971) Revêtements étales et Groupe Fondamental (SGA1), chapter VI: Catégories fibrées et descente, Lecture Notes in Math., vol 224. Springer-Verlag, Berlin
    • (1971) Lecture Notes in Math. , vol.224
    • Grothendieck, A.1
  • 100
    • 37649000023 scopus 로고    scopus 로고
    • Pursuing stacks
    • Maltsiniotis G (ed) Société Mathématique de France (to appear)
    • Grothendieck A (2007) Pursuing Stacks. In: Maltsiniotis G (ed) Documents Mathématiques, Société Mathématique de France (to appear)
    • (2007) Documents Mathématiques
    • Grothendieck, A.1
  • 103
    • 33748860345 scopus 로고    scopus 로고
    • Ontologies and worlds in category theory: Implications for neural systems
    • 1-2
    • Healy MJ, Caudell TP (2006) Ontologies and worlds in category theory: implications for neural systems. Axiomathes 16(1-2):165-214
    • (2006) Axiomathes , vol.16 , pp. 165-214
    • Healy, M.J.1    Caudell, T.P.2
  • 105
    • 0039846718 scopus 로고
    • Fibrations and quotients of differentiable groupoids
    • 1
    • Higgins PJ, Mackenzie KCH (1990) Fibrations and quotients of differentiable groupoids. J London Math Soc 42(1):101-110
    • (1990) J London Math Soc , vol.42 , pp. 101-110
    • Higgins, P.J.1    MacKenzie, K.C.H.2
  • 106
    • 14844339816 scopus 로고
    • Presentations of groupoids, with applications to groups
    • Higgins PJ (1964) Presentations of groupoids, with applications to groups. Proc Cambridge Philos Soc 60:7-20
    • (1964) Proc Cambridge Philos Soc , vol.60 , pp. 7-20
    • Higgins, P.J.1
  • 109
    • 77949891257 scopus 로고    scopus 로고
    • Can mind affect matter via active information?
    • 2
    • Hiley B, Pylkkänen P (2005) Can mind affect matter via active information? Mind Matter 3(2):7-27
    • (2005) Mind Matter , vol.3 , pp. 7-27
    • Hiley, B.1    Pylkkänen, P.2
  • 111
    • 0038157474 scopus 로고
    • On the concept of fiber spaces
    • Hurewicz E (1955) On the concept of fiber spaces. Proc Nat Acad Sci USA 41:956-961
    • (1955) Proc Nat Acad Sci USA , vol.41 , pp. 956-961
    • Hurewicz, E.1
  • 112
    • 37648999155 scopus 로고    scopus 로고
    • Non-abelian tensor products and non-abelian homology of groups
    • to appear
    • Innassaridze N (2002) Non-abelian tensor products and non-abelian homology of groups. J Pure Appl Algebra (to appear)
    • (2002) J Pure Appl Algebra
    • Innassaridze, N.1
  • 113
    • 0001626568 scopus 로고
    • On the connection between the fundamental groups of some related spaces
    • van Kampen EH (1933) On the connection between the fundamental groups of some related spaces. Am J Math 55:261-267
    • (1933) Am J Math , vol.55 , pp. 261-267
    • Van Kampen, E.H.1
  • 114
    • 0014421064 scopus 로고
    • Evolutionary rate at the molecular level
    • [1]
    • Kimura M (1968) Evolutionary rate at the molecular level. Nature 217:624-626 [1]
    • (1968) Nature , vol.217 , pp. 624-626
    • Kimura, M.1
  • 118
    • 0009032438 scopus 로고
    • The category of categories as a foundation for mathematics
    • Eilenberg S et al (eds) Springer-Verlag, Berlin
    • Lawvere FW (1966) The category of categories as a foundation for mathematics. In: Eilenberg S et al (eds) Proc conf categorical algebra-La Jolla. Springer-Verlag, Berlin, pp 1-20
    • (1966) Proc Conf Categorical Algebra-La Jolla , pp. 1-20
    • Lawvere, F.W.1
  • 119
    • 0000504637 scopus 로고
    • Functorial semantics of algebraic theories
    • Lawvere FW (1963) Functorial semantics of algebraic theories. Proc Natl Acad Sci USA, Math 50:869-872
    • (1963) Proc Natl Acad Sci USA, Math , vol.50 , pp. 869-872
    • Lawvere, F.W.1
  • 120
    • 37649022866 scopus 로고
    • Lecture held as a guest of the Romanian Academy of Sciences, Bucharest
    • Lawvere FW (1969) Closed Cartesian categories. Lecture held as a guest of the Romanian Academy of Sciences, Bucharest
    • (1969) Closed Cartesian Categories
    • Lawvere, F.W.1
  • 121
    • 51249189718 scopus 로고
    • An axiomatic explanation of complete self-reproduction
    • Löfgren L (1968) An axiomatic explanation of complete self-reproduction. Bull Maths Biophysics 30:317-348
    • (1968) Bull Maths Biophysics , vol.30 , pp. 317-348
    • Löfgren, L.1
  • 126
    • 9944243276 scopus 로고    scopus 로고
    • Cambridge University Press Cambridge, UK
    • Majid S (2002) A quantum groups primer. Cambridge University Press, Cambridge, UK
    • (2002) A Quantum Groups Primer
    • Majid, S.1
  • 130
    • 51249194645 scopus 로고
    • A logical calculus of ideas immanent in nervous activity
    • McCulloch W, Pitt W (1943) A logical calculus of ideas immanent in nervous activity. Bull Math Biophys 5:115-133
    • (1943) Bull Math Biophys , vol.5 , pp. 115-133
    • Pitt, W.1
  • 131
    • 0007255543 scopus 로고
    • Lyaponouv variables: Entropy and measurement in quantum mechanics
    • 10
    • Misra B, Prigogine I, Courbage M (1979) Lyaponouv variables: entropy and measurement in quantum mechanics. Proc Natl Acad Sci USA 78(10):4768-4772
    • (1979) Proc Natl Acad Sci USA , vol.78 , pp. 4768-4772
    • Misra, B.1    Prigogine, I.2    Courbage, M.3
  • 134
    • 37649022609 scopus 로고
    • On the definition of an abelian category
    • Ooort F (1970) On the definition of an abelian category. Proc Roy Neth Acad Sci 70:13-02
    • (1970) Proc Roy Neth Acad Sci , vol.70 , pp. 13-02
    • Ooort, F.1
  • 137
    • 0003353104 scopus 로고
    • Spinors in Hilbert space
    • Cambridge University Press, Cambridge
    • Plymen RJ, Robinson PL (1994) Spinors in Hilbert Space, Cambridge Tracts in Math, vol 114. Cambridge University Press, Cambridge
    • (1994) Cambridge Tracts in Math , vol.114
    • Plymen, R.J.1    Robinson, P.L.2
  • 138
    • 0012097809 scopus 로고    scopus 로고
    • Levels
    • 1-2
    • Poli R (1998) Levels. Axiomathes 9(1-2):197-211
    • (1998) Axiomathes , vol.9 , pp. 197-211
    • Poli, R.1
  • 139
    • 0012102691 scopus 로고    scopus 로고
    • The basic problem of the theory of levels of reality
    • 3-4
    • Poli R (2001a) The basic problem of the theory of levels of reality. Axiomathes 12(3-4):261-283
    • (2001) Axiomathes , vol.12 , pp. 261-283
    • Poli, R.1
  • 141
    • 33947721635 scopus 로고    scopus 로고
    • Levels of reality and the psychological stratum
    • Poli R (2006a) Levels of reality and the psychological stratum. Revue Internationale de Philosophie 61(2):163-180
    • (2006) Revue Internationale de Philosophie , vol.61 , Issue.2 , pp. 163-180
    • Poli, R.1
  • 142
    • 37649012589 scopus 로고    scopus 로고
    • Steps towards a synthetic methodology
    • Metanexus Institute, June 2006, Philadelphia, PA
    • Poli R (2006b) Steps towards a synthetic methodology. In: Proceed. conf. continuity and change: perspectives on science and religion. Metanexus Institute, June 2006, Philadelphia, PA http://www.metanexus.net/conferences/pdf/ conference2006/Poli.pdf
    • (2006) Proceed. Conf. Continuity and Change: Perspectives on Science and Religion
    • Poli, R.1
  • 143
    • 33947721296 scopus 로고    scopus 로고
    • First steps in experimental phenomenology
    • Loula A, Gudwin R (eds)
    • Poli R (2006c) First steps in experimental phenomenology. In: Loula A, Gudwin R (eds) Artificial cognition systems.
    • (2006) Artificial Cognition Systems
    • Poli, R.1
  • 144
    • 37649018352 scopus 로고    scopus 로고
    • Ontology: The categorical stance
    • Springer, Berlin(in press)
    • Poli R (2008) Ontology: the categorical stance. In: Theory and applications of ontology, vol 1. Springer, Berlin(in press)
    • (2008) Theory and Applications of Ontology , vol.1
    • Poli, R.1
  • 147
    • 0002145592 scopus 로고    scopus 로고
    • TFQTs from homotopy n-types
    • Porter T (1998) TFQTs from homotopy n-types. J London Math Soc 58:723-732
    • (1998) J London Math Soc , vol.58 , pp. 723-732
    • Porter, T.1
  • 149
    • 0000041163 scopus 로고
    • Théorie de Lie pour les groupoides différentiable, relation entre propriétes locales et globales
    • Pradines J (1966) Théorie de Lie pour les groupoides différentiable, relation entre propriétes locales et globales CR Acad Sci. Paris Sér A 268:907-910
    • (1966) CR Acad Sci Paris sér A , vol.268 , pp. 907-910
    • Pradines, J.1
  • 150
    • 0034373562 scopus 로고    scopus 로고
    • Quantisation of discretized spacetimes and the correspondence principle
    • Raptis I, Zapatrin RR (2000) Quantisation of discretized spacetimes and the correspondence principle. Intl Jour Theor Phys 39:1-89
    • (2000) Int J Theor Phys , vol.39 , pp. 1-89
    • Raptis, I.1    Zapatrin, R.R.2
  • 151
    • 51649202150 scopus 로고
    • The representation of organisms in terms of predicates
    • Rashevsky N (1965) The representation of organisms in terms of predicates. Bull Math Biophys 27:477-491
    • (1965) Bull Math Biophys , vol.27 , pp. 477-491
    • Rashevsky, N.1
  • 152
    • 0014478928 scopus 로고
    • Outline of a unified approach to physics, biology and sociology
    • Rashevsky N (1969) Outline of a unified approach to physics, biology and sociology. Bull Math Biophys 31:159-198
    • (1969) Bull Math Biophys , vol.31 , pp. 159-198
    • Rashevsky, N.1
  • 153
    • 0011502993 scopus 로고
    • Über Identitäten von Relationen
    • Reidermeister K (1949) Über Identitäten von Relationen. Abh Math Sem Hamburg 16:114-118
    • (1949) Abh Math Sem Hamburg , vol.16 , pp. 114-118
    • Reidermeister, K.1
  • 154
    • 33749264099 scopus 로고    scopus 로고
    • More lectures on algebraic quantum field theory
    • Springer Berlin
    • Roberts JE (2004) More lectures on algebraic quantum field theory. In: Connes A et al (eds) Noncommutative geometry. Springer, Berlin
    • (2004) Noncommutative Geometry
    • Roberts, J.E.1    Connes, A.2
  • 156
    • 51649219090 scopus 로고
    • A relational theory of biological systems
    • Rosen R (1958a) A relational theory of biological systems. Bull Math Biophys 20:245-260
    • (1958) Bull Math Biophys , vol.20 , pp. 245-260
    • Rosen, R.1
  • 157
    • 51649204660 scopus 로고
    • The representation of biological systems from the standpoint of the theory of categories
    • Rosen R (1958b) The representation of biological systems from the standpoint of the theory of categories. Bull Math Biophys 20:317-341
    • (1958) Bull Math Biophys , vol.20 , pp. 317-341
    • Rosen, R.1
  • 158
    • 0022079212 scopus 로고
    • On complex systems
    • Rosen R (1987) On complex systems. Eur J Operat Res 30:129-134
    • (1987) Eur J Operat Res , vol.30 , pp. 129-134
    • Rosen, R.1
  • 159
    • 0003912894 scopus 로고    scopus 로고
    • Columbia University Press, New York
    • Rosen R (1999) Essays on life itself. Columbia University Press, New York
    • (1999) Essays on Life Itself
    • Rosen, R.1
  • 163
    • 0039756734 scopus 로고
    • Finitary substitute for continuous topology
    • 7
    • Sorkin RD (1991) Finitary substitute for continuous topology. Int J Theor Phys 30(7):923-947
    • (1991) Int J Theor Phys , vol.30 , pp. 923-947
    • Sorkin, R.D.1
  • 167
    • 0003720769 scopus 로고
    • Dover Publications Inc. New York
    • Thompson W D'Arcy (1994) On growth and form. Dover Publications Inc., New York
    • (1994) On Growth and Form
    • Wd'Arcy, T.1
  • 168
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • Turing AM (1952) The chemical basis of morphogenesis. Philoso Trans Royal Soc (B) 257:37-72
    • (1952) Philos Trans Royal Soc (B) , vol.257 , pp. 37-72
    • Turing, A.M.1
  • 172
    • 0000137650 scopus 로고    scopus 로고
    • Groupoids: Unifying internal and external symmetry
    • Weinstein A (1996) Groupoids: unifying internal and external symmetry. Notices of the Amer Math Soc 43:744-752
    • (1996) Notices Am Math Soc , vol.43 , pp. 744-752
    • Weinstein, A.1
  • 174
    • 0003684962 scopus 로고
    • (publ. 2000). Cambridge University Press, Cambridge, UK
    • Weinberg S (1995) The quantum theory of fields I & II (vol. III publ. 2000). Cambridge University Press, Cambridge, UK
    • (1995) The Quantum Theory of Fields i & Ii , vol.3
    • Weinberg, S.1
  • 176
    • 0001592411 scopus 로고
    • On adding relations to homotopy groups
    • 2
    • Whitehead JHC (1941) On adding relations to homotopy groups. Ann Math 42(2):409-428
    • (1941) Ann Math , vol.42 , pp. 409-428
    • Whitehead, J.H.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.