Avoiding the axiom of choice in general category theory

Journal of Pure and Applied Algebra

Volumn 108, Issue 2, 1996, Pages 109-173

  Makkai, M ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030597685     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/0022-4049(95)00029-1     Document Type: Article

References (18)

1. [1] J. Benabou, Introduction to bicategories. in: Reports of the Midwest Category Seminar, Lecture Notes in Mathematics, Vol. 47 (Springer, Berlin, 1967) 1-77.
2. [2] J. Benabou, Fibered categories and the foundations of naive category theory, J. Symbolic Logic 50 (1985) 10-37.
3. [3] A. Blass, Injectivity, projectivity, and the axiom of choice, Trans. Amer. Math. Soc. 255 (1979) 31-59.
4. [4] S. Eilenberg and G.M. Kelly, Closed categories, in: Proc. Conf. on Categorical Algebra, La Jalla, 1965 (Springer, Berlin, 1966) 421-562.
5. [5] P.J. Freyd and A. Scedrov, Categories, Allegories, North-Holland Mathematical Library, Vol. 39 (North-Holland, Amsterdam, 1990).
6. [6] P. Gabriel and F. Ulmer, Lokal präsentierbare Kategorien, Lecture Notes in Mathematics, Vol. 221, (Springer, Berlin, 1971).
7. [7] K. Gödel, The Consistency of the Continuum Hypothesis, Ann. Math. Studies, Vol. 3 (Princeton Univ. Press, Princeton, NJ, 1940).
8. [8] T. Jech, Set Theory (Academic Press, New York, 1978).
9. [9] P.T. Johnstone, Topos Theory (Academic Press, New York, 1977).
10. [10] A. Joyal and R. Street, The geometry of tensor calculus, Adv. Math. 88 (1991) 55-112.
11. [11] S. Mac Lane, Categories for the Working Mathematician (Springer, Berlin, 1971).
12. [12] M. Makkai, Stone duality for first order logic, Adv. Math. 65 (1987) 97-170.
13. [13] M. Makkai, Contributions to the theory of doctrines, in preparation.
14. [14] M. Makkai, Generalized sketches as a framework for completeness theorems. J. Pure Appl. Algebra, to appear.
15. [15] M. Makkai and R. Pare, Anafunctors and indexed category theory, in preparation.
16. [16] J. Penon, Theories de categories, Diagrammes 2 (1979) P.1-P.54.
17. [17] R. Pare and D. Schumacher, Abstract families and the adjoint functor theorem, in: P.T. Johnstone and R. Pare, eds., Indexed Categories and their Applications, Lecture Notes in Mathematics, Vol. 661 (Springer, Berlin, 1978) 1-125.
18. [18] R. Street, Fibrations in bicategories, Cahiers Top. Geom. Diff. 21 (1980) 11-160.