Elementary categories, elementary toposes
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چکیده
منابع مشابه
Relating First-order Set Theories and Elementary Toposes
We show how to interpret the language of first-order set theory in an elementary topos endowed with, as extra structure, a directed structural system of inclusions (dssi). As our main result, we obtain a complete axiomatization of the intuitionistic set theory validated by all such interpretations. Since every elementary topos is equivalent to one carrying a dssi, we thus obtain a first-order s...
متن کاملfirst - order set theories , toposes and categories of classes
This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions (dssi) on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conserv...
متن کاملElementary Axioms for Local Maps of Toposes
We present a complete elementary axiomatization of local maps of toposes.
متن کاملMolecular Toposes*
In [2], Barr and Diaconescu characterized those Grothendieck toposes 8 for which the inverse image, A, of the geometric morphism r: 8 + Yet, is logical. It was shown (among other things) that this happens precisely when the lattice of subobjects of every object of 8 is a complete atomic boolean algebra. Toposes satisfying this property are called atomic. These results were relativised to the ca...
متن کاملA Representation Theorem for Geometric Morphisms
It it shown that geometric morphisms between elementary toposes can be represented as certain adjunctions between the corresponding categories of locales. These adjunctions are characterized by (i) they preserve the order enrichment and the Sierpiński locale, and (ii) they satisfy Frobenius reciprocity.
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تاریخ انتشار 1992