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Abstract: Introduction Category theory can be viewed as an elementary, i.e. essentially first order, theory independent from set theory. In an elementary topos, i.e. a category satisfying a number of elementary axioms, one can perform all constructions that one performes with sets in everyday mathematics. Nevertheless, the language of category theory is not expressive enough to capture those categorical notions that make reference to set theory. Amongst those are: (co-)completeness, (local) smallness,... (Update)
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BibTeX entry: (Update)
P. Lietz. A fibrational theory of geometric morphisms. Master's thesis, TU Darmstadt, May 1998. http://citeseer.ist.psu.edu/lietz98fibrational.html More
@mastersthesis{ lietz98fibrational,
author = "Peter Lietz",
title = "A Fibrational Theory of Geometric Morphisms",
year = "1998",
url = "citeseer.ist.psu.edu/lietz98fibrational.html" }
Citations (may not include all citations):83 Topos Theory (context) - Johnstone - 1977
80 Handbook of Categorical Algebra (context) - Borceux - 1994
48 Introduction to extensive and distributive categories (context) - Carboni, Lack et al. - 1993
20 Abstract families and the adjoint functor theorems (context) - Par'e, Schumacher - 1978
14 Fibred categories and the foundations of naive category theo.. (context) - B'enabou - 1985
7 A First Introduction to Topos Theory (context) - MacLane, Moerdijk et al. - 1992
1 Charact'erisation des topos de faisceaux sur un site interne.. (context) - Moens - 1982
1 Descent for Cocomplete Categories (context) - Funk - 1990
1 Fibrations Geometriques et Theoreme de Giraud (context) - Moens - 1982
1 Categorical Logic & Type Theory (context) - Jacobs
1 Des Cat'egories Fibr'ees (context) - B'enabou - 1980
1 Geometric Morphisms and Indexed Toposes (context) - Jibladze
1 A Fibrational View of Geometric Morphisms - Streicher - 1997
1 Some remarks on 2-categorical algebra (context) - B'enabou - 1989
1 Number 21 in Logic Guides (context) - McLarty, Elementary - 1992
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