A 2 -categorical approach to change of base and geometric morphisms I

A. Carboni; G. M. Kelly; R. J. Wood

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1991)

  • Volume: 32, Issue: 1, page 47-95
  • ISSN: 1245-530X

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Carboni, A., Kelly, G. M., and Wood, R. J.. "A $2$-categorical approach to change of base and geometric morphisms I." Cahiers de Topologie et Géométrie Différentielle Catégoriques 32.1 (1991): 47-95. <http://eudml.org/doc/91471>.

@article{Carboni1991,
author = {Carboni, A., Kelly, G. M., Wood, R. J.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {enriched category; biadjunction; lax functor; adjointness; 2-categories; Ord-categories; Cartesian bicategories; bicategories of relations in regular categories},
language = {eng},
number = {1},
pages = {47-95},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {A $2$-categorical approach to change of base and geometric morphisms I},
url = {http://eudml.org/doc/91471},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Carboni, A.
AU - Kelly, G. M.
AU - Wood, R. J.
TI - A $2$-categorical approach to change of base and geometric morphisms I
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1991
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 32
IS - 1
SP - 47
EP - 95
LA - eng
KW - enriched category; biadjunction; lax functor; adjointness; 2-categories; Ord-categories; Cartesian bicategories; bicategories of relations in regular categories
UR - http://eudml.org/doc/91471
ER -

References

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  1. [1] J. Bénabou, Introduction to bicategories, Lecture Notes in Math.47, Springer (1967), 1-77. MR220789
  2. [2] R. Betti and A.J. Power, On local adjointness of distributive bicategories, Boll. Unione Mat. Italiana (7) 2-B (1988), 931-947. Zbl0665.18007MR977597
  3. [3] A. Carboni, S. Kasangian and R. Street, Bicategories of spans and relations, J. Pure Appl. Algebra33 (1984), 259-267. Zbl0577.18005MR761632
  4. [4] A. Carboni, G.M. Kelly and R.J. Wood, A 2-categorical approach to geometric morphisms I, University of Sydney Research Report 89-19 (October 1989). Zbl0747.18008
  5. [5] A. Carboni and R. Street, Order ideals in categories, Pacific J. Math.124 (1986), 275-288. Zbl0565.18001MR856163
  6. [6] A. Carboni and R.F.C. Walters, Cartesian bicategories I, J. Pure Appl. Algebra49 (1987), 11-32. Zbl0637.18003MR920513
  7. [7] S. Eilenberg and G.M. Kelly, Closed categories, in Proc. Conf. on Categorical Algebra (La Jolla1965), Springer (1966), 421-562. Zbl0192.10604MR225841
  8. [8] J.W. Gray, Formal category theory: adjointness for 2-categories, Lecture Notes in Math.391, Springer (1974). Zbl0285.18006MR371990
  9. [9] J.W. Gray, Closed categories, lax limits and homotopy limits, J. Pure Appl. Algebra19 (1980), 127-158. Zbl0462.55008MR593251
  10. [10] C.B. Jay, Local adjunctions, J. Pure Appl. Algebra53 (1988), 227-238. Zbl0673.18006MR961361
  11. [11] A. Joyal and R. Street, Braided monoidal categories, Macquarie Math Reports 860081, Nov. 1986. 
  12. [12] A. Joyal and M. Tierney, An extension of the Galois theory of Grothendieck, Memoirs Amer. Math. Soc.51 (1984), No. 309. Zbl0541.18002MR756176
  13. [13] G.M. Kelly, Monomorphisms, epimorphisms, and pull-backs, J. Austral. Math. Soc.9 (1969), 124-142. Zbl0169.32604MR240161
  14. [14] G.M. Kelly, Doctrinal adjunction, Lecture Notes in Math.420, Springer (1974), 257-280. Zbl0334.18004MR360749
  15. [15] G.M. Kelly, Basic Concepts of Enriched Category Theory, London Math. Soc. Lecture Notes Series64, Cambridge Univ. Press (1982). Zbl0478.18005MR651714
  16. [16] G.M. Kelly and R. Street, Review of the elements of 2-categories, Lecture Notes in Math.420, Springer (1974), 75-103. Zbl0334.18016MR357542
  17. [17] F.W. Lawvere, Metric spaces, generalized logic, and closed categories, Rend. del Sem. Mat. e Fis. di Milano43 (1973), 135-166. Zbl0335.18006MR352214
  18. [18] A.M. Ptits, Applications of sup-lattice enriched category theory to sheaf theory, Proc. London Math. Soc.57 (1988), 433-480. Zbl0619.18005MR960096
  19. [19] R. Rosebrugh and R.J. Wood, Cofibrations in the bicategory of topoi, J. Pure Appl. Algebra32 (1984), 71-94. Zbl0535.18006MR739640
  20. [20] R. Rosebrugh and R.J. Wood, Proarrows and cofibrations, J. Pure Appl. Algebra53 (1988), 271-296. Zbl0673.18008MR961365
  21. [21] R.F.C. Walters, Sheaves and Cauchy-complete categories, Cahiers Top. Geom. Diff. Cat.XXII (1981), 283-286. Zbl0495.18009MR649076
  22. [22] R.F.C. Walters, Sheaves on sites as Cauchy-complete categories, J. Pure Appl. Algebra24 (1982), 95-102. Zbl0497.18016MR647583
  23. [23] R.J. Wood, Abstract proarrows I, Cahiers Top. Geom. Diff. Cat.XXIII (1982), 279-290. Zbl0497.18012MR675339
  24. [24] R.J. Wood, Proarrows Ii, Cahiers Top. Geom. Diff. Cat.XXVI (1985), 135-168. Zbl0583.18003MR794752

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