Generic commutative separable algebras and cospans of graphs

Theory and Applications of Categories

Volumn 15, Issue 6, 2005, Pages

  Rosebrugh, R ^a   Sabadini, N ^a   Walters, R F C ^a  

^a NONE

Author keywords

Cospan category; Separable algebra

Indexed keywords

EID: 27844590338     PISSN: 1201561X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. L. Abrams, Two dimensional topological quantum field theories and Frobenius algebras, J. Knot Theory Ramifications, 5, 569-587, 1996.
2. J. Beck, Distributive laws, in Seminar on Triples and Categorical Homology Theory, Lecture Notes in Mathematics, 80, pages 119-140, Springer-Verlag, 1969.
3. R. Betti, A. Carboni, R.H. Street and R.F.C. Walters, Variation through enrichment, Journal of Pure and Applied Algebra, 29, 109-127, 1983.
4. A. Carboni, R.F.C. Walters, Cartesian Bicategories I, J. Pure Applied Algebra, 49, 11-32, 1987.
5. A. Carboni, Matrices, relations and group representations, J. Algebra, 138, 497-529, 1991.
6. F. DeMeyer, E. Ingraham, Separable algebra over commutative rings, Springer Lecture Notes in Mathematics, 181, 1971.
7. F. Gadducci, R. Heckel, An inductive view of graph transformation, Springer LNCS, 1376, 223-237, 1997.
8. F. Gadducci, R. Heckel, M. Llabres, A bi-categorical axiomatisation of concurrent graph rewriting, ENTCS, 29, 1999.
9. R. Gates, On generic separable objects, Theory and Applications of Categories, 4, 204-248, 1998.
10. A. Joyal, R.H. Street, D. Verity, Traced monoidal categories, Math. Proc. Cambridge Philosophical Soc. 119 (3), 425-446, 1996.
11. P. Katis, N. Sabadini, R.F.C. Walters, Span(Graph): A categorical algebra of transition systems, Proc. AMAST '97, SLNCS 1349, 307-321, Springer Verlag, 1997.
12. P. Katis, N. Sabadini, R.F.C. Walters, On the algebra of systems with feedback and boundary, Rendiconti del Circolo Matematico di Palermo Serie II, Suppl. 63, 123-156, 2000.
13. P. Katis, N. Sabadini, R.F.C. Walters, A formalisation of the IWIM Model, in: Proc. COORDINATION 2000, (Eds.) A. Porto, G.-C. Roman, LNCS 1906, 267-283, Springer Verlag, 2000.
14. P. Katis, N. Sabadini, R.F.C. Walters, Feedback, trace and fixed-point semantics, Theoret. Informatics Appl. 36, 181-194, 2002.
15. J. Kock, Frobenius algebras and 2D topological Quantum Field Theories, Cambridge University Press, 2004.
16. F. W. Lawvere, Ordinal sums and equational doctrines, Springer Lecture Notes in Mathematics, 80, 141-155, 1967.
17. S. Lack, Composing PROPs, Theory and Applications of Categories, 13, 147-163, 2004.
18. E.H. Moore, Concerning the abstract group of order k! and 1/2k!, Proc. London Math. Soc, 28, 357-366, 1897.
19. J. Meseguer, U. Montanari, Petri Nets are Monoids, Information and Computation, 88, 105-155, 1990. Also SRI-CSL-88-3, January 1988.
20. R. Rosebrugh, N. Sabadini, R.F.C. Walters, Minimization and minimal realization in Span(Graph), Mathematical Structures in Computer Science, 14, 685-714, 2004.
21. R. Rosebrugh, N. Sabadini, R.F.C. Walters, Symmetric separable algebras in monoidal categories and Cospan(Graph), Abstracts of the International Category Theory Conference, CT'04, Vancouver 2004.
22. R. Rosebrugh, R.J. Wood, Factorization Systems and Distributive Laws, J. Pure Appl. Alg. 175, 327-353, 2002.
23. N. Sabadini, R.F.C. Walters, Hierarchical automata and P systems, CATS'03, ENTCS 78, 2003.
24. P. Sobocinski, Process congruences from reaction rules, in Luca Aceto's "Concurrency Column", Bulletin of the EATCS vol. 84, 2004.
25. R.F.C. Walters, The tensor product of matrices, Lecture, International Conference on Category Theory, Louvain-la-Neuve, 1987.