Yoneda structures from 2-toposes

Applied Categorical Structures

Volumn 15, Issue 3, 2007, Pages 259-323

  Weber, Mark ^a  

^a MACQUARIE UNIVERSITY   (Australia)

Author keywords

2 topos; Fibration; Internal category theory; Yoneda structure

Indexed keywords

GLOBAL OPTIMIZATION; MATERIALS SCIENCE; STRUCTURAL ANALYSIS;

2-TOPOS; FIBRATION; INTERNAL CATEGORY THEORY; YONEDA STRUCTURE;

TOPOLOGY;

EID: 34547251664     PISSN: 09272852     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10485-007-9079-2     Document Type: Article

References (31)

1. Baez, I. Crans, A.: Higher-dimensional algebra VI: Lie 2-algebras. Theory Appl. Categ. 12, 492-528 (2004)
2. Baez, J., Dolan, J.: Higher-dimensional algebra and topological quantum field theory. J. Math. Phys. 36, 6073-6105 (1995)
3. Baez, J., Dolan, J.: Higher-dimensional algebra III: n-categories and the algebra of opetopes. Adv. Math. 135, 145-206 (1998)
4. Baez, J., Lauda, A.: Higher-dimensional algebra V: 2-groups. Theory Appl. Categ. 12, 423-491 (2004)
5. Baez, J., Schreiber, U.: Higher gauge theory. arXiv:math.DG/0511710 (2005)
6. Batanin, M.: Computads for unitary monads on globular sets. Contemp. Math. 230, 37-57 (1998)
7. Batanin, M.: Monoidal globular categories as a natural environment for the theory of weak n-categories. Adv. Math. 136, 39-103 (1998)
8. n-spaces. arXivmath. CT/0207281 (2002)
9. Batanin, M.: The combinatorics of iterated loop spaces. arXiv:math.CT/0301221 (2003)
10. Bénabou, J.: Fibred categories and the foundation of naive category theory. J. Symbolic Logic 50, 10-37 (1985)
11. Bourn, D.: Sur les ditopos. C. R. Acad. Sci. Paris 279, 911-913 (1974)
12. Carboni, A., Johnstone, P.T.: Connected limits, familial representability and Artin glueing. Math. Structures Comput. Sci. 5, 441-459 (1995)
13. Ehresmann, C.: Gattungen von lokalen Strukturen. Jber. Deutsch. Math. Verein 60, 49-77 (1958)
14. Freyd, P., Street, R.: On the size of categories. Theory Appl. Categ. 1, 174-181 (1995)
15. Gray, J.W.: Fibred and cofibred categories. In: Proceedings Conference on Categorical Algebra at La Jolla, pp. 21-83. Springer, Berlin (1966)
16. Grothendieck, A.: Catégories fibrées et descente. Lecture Notes in Math. 224, 145-194 (1970)
17. Hermida, C.: Some properties of fib as a fibred 2-category. JPAA 134(1), 83-109 (1999)
18. Johnstone, P.T.: Sketches of an elephant: a topos theory compendium. In: Oxford Logic Guides, vol. 1. Oxford Science, Oxford, UK (2002)
19. Kelly, G.M.: Basic concepts of enriched category theory. In: LMS Lecture Note Series, vol. 64. Cambridge University Press, Cambridge (1982)
20. Kelly, G.M., Street, R.: Review of the elements of 2-categories. Lecture Notes in Math. 420, 75-103 (1974)
21. Lawvere, F.W.: Equality in hyperdoctrines and comprehension schema as an adjoint functor. In: Proceedings of the American Mathematical Society Symposium on Pure Mathematics, vol. XVII, pp. 1-14 (1970)
22. Mac Lane, S., Moerdijk, I.: Sheaves in Geometry and Logic. Springer, Berlin (1991)
23. Penon, J.: Sous-catégories classifiée. C. R. Acad. Sci. Paris 278, 475-477 (1974)
24. Street, R.: Elementary cosmoi. Lecture Notes in Math. 420, 134-180 (1974)
25. Street, R.: Fibrations and Yoneda's lemma in a 2-category. Lecture Notes in Math. 420, 104-133 (1974)
26. Street, R.: Limits indexed by category-valued 2-functors. J. Pure Appl. Algebra 8, 149-181 (1976)
27. Street, R.: Cosmoi of internal categories. Trans. Amer. Math. Soc. 258, 271-318 (1980)
28. Street, R.: Fibrations in bicategories. Cahiers Topologie. Géom. Differentielle Catégo. 21, 111-160 (1980)
29. Street, R.: The petit topos of globular sets. J. Pure Appl. Algebra 154, 299-315 (2000)
30. Street, R., Walters, R.F.C.: Yoneda structures on 2-categories. J. Algebra 50, 350-379 (1978)
31. Weber, M.: Operads within monoidal pseudo algebra II (in preperation)