메뉴 건너뛰기




Volumn 5, Issue 4, 1997, Pages 363-413

Categorically Algebraic Foundations for Homotopical Algebra

Author keywords

(co)cylinder; 2 categories; Abstract homotopy theory; Connections; Cubical objects; Homotopical algebra; Homotopy; Homotopy (co)limits; Internal monoids; Presheaves; Sheaves; Slice categories

Indexed keywords


EID: 0001242466     PISSN: 09272852     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008620005400     Document Type: Article
Times cited : (21)

References (30)
  • 2
    • 0001307082 scopus 로고
    • Abstract homotopy theory and generalised sheaf cohomology
    • Brown, K. S.: Abstract homotopy theory and generalised sheaf cohomology, Trans. Amer. Math. Soc. 186 (1973), 419-458.
    • (1973) Trans. Amer. Math. Soc. , vol.186 , pp. 419-458
    • Brown, K.S.1
  • 4
    • 0001897227 scopus 로고
    • Colimit theorems for relative homotopy groups
    • Brown, R. and Higgins, P. J.: Colimit theorems for relative homotopy groups, J. Pure Appl. Algebra 22 (1981), 11-41.
    • (1981) J. Pure Appl. Algebra , vol.22 , pp. 11-41
    • Brown, R.1    Higgins, P.J.2
  • 5
    • 0003324952 scopus 로고
    • Tensor products and homotopies for ω-groupoids and crossed complexes
    • Brown, R. and Higgins, P. J.: Tensor products and homotopies for ω-groupoids and crossed complexes, J. Pure Appl. Algebra 47 (1987), 1-33.
    • (1987) J. Pure Appl. Algebra , vol.47 , pp. 1-33
    • Brown, R.1    Higgins, P.J.2
  • 6
    • 0001301955 scopus 로고
    • Van Kampen theorems for diagrams of spaces
    • Brown, R. and Loday, J. L.: Van Kampen theorems for diagrams of spaces, Topology 26 (1987), 311-335.
    • (1987) Topology , vol.26 , pp. 311-335
    • Brown, R.1    Loday, J.L.2
  • 7
    • 0003173315 scopus 로고
    • Homotopy and homology of diagrams of spaces
    • Seattle 1985, Lecture Notes in Math. 1286, Springer-Verlag
    • Dror Farjoun, E.: Homotopy and homology of diagrams of spaces, in Algebraic Topology, Proceedings, Seattle 1985, Lecture Notes in Math. 1286, Springer-Verlag, 1987, pp. 93-134.
    • (1987) Algebraic Topology, Proceedings , pp. 93-134
    • Dror Farjoun, E.1
  • 8
    • 0002539075 scopus 로고
    • On the categorical foundations of homological and homotopical algebra
    • Grandis, M.: On the categorical foundations of homological and homotopical algebra, Cahiers Top. Géom. Diff. Catég. 33 (1992), 135-175.
    • (1992) Cahiers Top. Géom. Diff. Catég. , vol.33 , pp. 135-175
    • Grandis, M.1
  • 9
    • 0001110647 scopus 로고
    • Homotopical algebra in homotopical categories
    • Grandis, M.: Homotopical algebra in homotopical categories, Appl. Categorical Structures 2 (1994), 351-406.
    • (1994) Appl. Categorical Structures , vol.2 , pp. 351-406
    • Grandis, M.1
  • 10
    • 0000900682 scopus 로고
    • Cubical monads and their symmetries
    • Proceedings of the 11th International Conference on Topology, Trieste 1993
    • Grandis, M.: Cubical monads and their symmetries, in Proceedings of the 11th International Conference on Topology, Trieste 1993, Rend. Ist. Mat. Univ. Trieste 25 (1993), pp. 223-268.
    • (1993) Rend. Ist. Mat. Univ. Trieste , vol.25 , pp. 223-268
    • Grandis, M.1
  • 11
    • 0002644932 scopus 로고    scopus 로고
    • Cubical homotopical algebra and cochain algebras
    • Grandis, M.: Cubical homotopical algebra and cochain algebras, Ann. Mat. Pura Appl. 170 (1996), 147-186.
    • (1996) Ann. Mat. Pura Appl. , vol.170 , pp. 147-186
    • Grandis, M.1
  • 12
    • 84971116292 scopus 로고
    • Homotopical algebra and triangulated categories
    • Grandis, M.: Homotopical algebra and triangulated categories, Math. Proc. Cambridge Philos. Soc. 118 (1995), 259-295.
    • (1995) Math. Proc. Cambridge Philos. Soc. , vol.118 , pp. 259-295
    • Grandis, M.1
  • 13
    • 0010052751 scopus 로고
    • Sheaves with values in a category
    • Gray, J. W.: Sheaves with values in a category, Topology 3 (1965), 1-18.
    • (1965) Topology , vol.3 , pp. 1-18
    • Gray, J.W.1
  • 15
    • 1842767836 scopus 로고
    • Track homotopy over a fixed space
    • Hardie, K. A. and Kamps, K. H.: Track homotopy over a fixed space, Glasnik Mat. 24 (1989), 161-179.
    • (1989) Glasnik Mat. , vol.24 , pp. 161-179
    • Hardie, K.A.1    Kamps, K.H.2
  • 17
    • 0342462644 scopus 로고
    • The coherent homotopy category over a fixed space is a category of fractions
    • Hardie, K. A., Kamps, K. H., and Porter, T.: The coherent homotopy category over a fixed space is a category of fractions, Topology Appl. 40 (1991), 265-274.
    • (1991) Topology Appl. , vol.40 , pp. 265-274
    • Hardie, K.A.1    Kamps, K.H.2    Porter, T.3
  • 18
    • 84968510172 scopus 로고
    • Stable homotopy categories
    • Heller, A.: Stable homotopy categories, Bull. Amer. Math. Soc. 74 (1968), 28-63.
    • (1968) Bull. Amer. Math. Soc. , vol.74 , pp. 28-63
    • Heller, A.1
  • 19
    • 84972529845 scopus 로고
    • Ex homotopy theory I
    • James, I. M.: Ex homotopy theory I, Ill. J. Math. 15 (1971), 329-345.
    • (1971) Ill. J. Math. , vol.15 , pp. 329-345
    • James, I.M.1
  • 21
    • 2342475722 scopus 로고
    • Über einige formale Eigenschaften von Faserungen und h-Faserungen
    • Kamps, K. H.: Über einige formale Eigenschaften von Faserungen und h-Faserungen, Manuscripta Math. 3 (1970), 237-255.
    • (1970) Manuscripta Math. , vol.3 , pp. 237-255
    • Kamps, K.H.1
  • 22
    • 0042185389 scopus 로고
    • Kan-Bedingungen und abstrakte Homotopietheorie
    • Kamps, K. H.: Kan-Bedingungen und abstrakte Homotopietheorie, Math. Z. 124 (1972), 215-236.
    • (1972) Math. Z. , vol.124 , pp. 215-236
    • Kamps, K.H.1
  • 24
  • 27
    • 0000626516 scopus 로고
    • Algebraic classification of equivariant homotopy 2-types, I
    • Moerdijk, I. and Svensson, J. A.: Algebraic classification of equivariant homotopy 2-types, I, J. Pure Appl. Algebra 89 (1993), 187-216.
    • (1993) J. Pure Appl. Algebra , vol.89 , pp. 187-216
    • Moerdijk, I.1    Svensson, J.A.2
  • 28
    • 0000980011 scopus 로고
    • Homotopiemengen und ihre induzierten Abbildungen, I
    • Puppe, D.: Homotopiemengen und ihre induzierten Abbildungen, I, Math. Z. 69 (1958), 299-344.
    • (1958) Math. Z. , vol.69 , pp. 299-344
    • Puppe, D.1
  • 30
    • 0041886193 scopus 로고
    • Pullback and pushout squares in a special double category with connection
    • Spencer, C. B. and Wong, Y. L.: Pullback and pushout squares in a special double category with connection, Cahiers Top. Géom. Diff. Catég. 24 (1983), 161-192.
    • (1983) Cahiers Top. Géom. Diff. Catég. , vol.24 , pp. 161-192
    • Spencer, C.B.1    Wong, Y.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.