Metric, topology and multicategory - A common approach

Journal of Pure and Applied Algebra

Volumn 179, Issue 1-2, 2003, Pages 13-47

  Clementino, Maria Manuel ^a   Tholen, Walter ^b  

^a Departamento de Matemática   (Portugal)

^b YORK UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037396525     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(02)00246-3     Document Type: Article

References (26)

1. M. Barr, Relational algebras, in: Lecture Notes in Mathematics, Vol. 137, Springer, Berlin, 1970, pp. 39-55.
2. J. Bénabou, Introduction to bicategories, in: Lecture Notes in Mathematics, Vol. 47, Springer, Berlin, 1967.
3. R. Betti, A. Carboni, R. Street, R. Walters, Variation through enrichment, J. Pure Appl. Algebra 29 (1983) 109-127.
4. F. Borceux, Handbook of Categorical Algebra 2: Categories and Structures, Cambridge University Press, Cambridge, 1994.
5. R. Börger, Coproducts and ultrafilters, J. Pure Appl. Algebra 46 (1987) 35-47.
6. R. Börger, W. Tholen, Strong, regular and dense generators, Cahiers Topologie Géom. Différentielle Catégoriques 32 (1991) 257-276.
7. A. Burroni, T-categories, Cahiers Topologie Géom. Différentielle 12 (1971) 215-321.
8. M.M. Clementino, D. Hofmann, Topological features of lax algebras, Applied Cat. Struct., to appear.
9. M.M. Clementino, D. Hofmann, W. Tholen, The convergence approach to exponentiable maps, Port. Math., to appear.
10. M.M. Clementino, D. Hofmann, W. Tholen, Exponentiability in categories of (T,V)-algebras, in preparation.
11. S. Eilenberg, G.M. Kelly, Closed categories, in: Proceedings of the Conference Categorical Algebra, La Jolla, CA, 1965, Springer, New York, 1966, pp. 421-562.
12. S. Eilenberg, J.C. Moore, Adjoint functors and triples, Illinois J. Math. 9 (1965) 381-398.
13. C. Hermida, Representable multicategories, Adv. in Math. 151 (2000) 164-225.
14. C. Hermida, M. Makkai, J. Power, On weak higher-dimensional categories I-2, J. Pure Appl. Algebra 157 (2001) 247-277.
15. G.M. Kelly, Basic concepts of enriched category theory, in: London Mathematical Society Lecture Notes, Vol. 64, Cambridge University Press, Cambridge, 1982.
16. S. Lack, R. Street, The formal theory of monads II, J. Pure Appl. Algebra 175 (2002) 243-265.
17. J. Lambek, Deductive systems in categories, III, in: Lecture Notes in Mathematics, Vol. 86, Springer, Berlin, 1969, pp. 76-122.
18. J. Lambek, Multicategories revisited, in: Contemporary Mathematics, Vol. 92, American Mathematical Society, Providence, 1989, pp. 217-239.
19. F.W. Lawvere, Metric spaces, generalized logic, and closed categories, Rend. Sem. Mat. Fis. Milano 43 (1973) 135-166.
20. T. Leinster, General operads and multicategories, preprint, 1997. arxiv.org/abs/math.ct/9810053
21. R. Lowen, Approach Spaces: the Missing Link in the Topology-Uniformity-Metric Triad, Oxford Mathematical Monographs, Oxford University Press, Oxford, 1997.
22. E.G. Manes, A triple theoretic construction of compact algebras, in: Lecture Notes in Mathematics, Vol. 80, Springer, Berlin, 1969, pp. 91-118.
23. C. Pisani, Convergence in exponentiable spaces, Theory Appl. Categories 5 (1999) 148-162.
24. R.D. Rosebrugh, R.J. Wood, Distributive laws and factorization, J. Pure Appl. Algebra 175 (2002) 327-353.
25. J. Rosický, W. Tholen, Lax factorization algebras, J. Pure Appl. Algebra 175 (2002) 355-382.
26. W. Tholen, Injectives, exponentials, and model categories, in: Abstracts of the International Conference on Category Theory, Como, Italy, 2000, pp. 183-190.