A Note on the Exact Completion of a Regular Category, and Its Infinitary Generalizations
نویسندگان
چکیده
A new description of the exact completion Cex/reg of a regular category C is given, using a certain topos Shv(C) of sheaves on C; the exact completion is then constructed as the closure of C in Shv(C) under finite limits and coequalizers of equivalence relations. An infinitary generalization is proved, and the classical description of the exact completion is derived.
منابع مشابه
A Note on Free Regular and Exact Completions and Their Infinitary Generalizations
Free regular and exact completions of categories with various ranks of weak limits are presented as subcategories of presheaf categories. Their universal properties can then be derived with standard techniques as used in duality theory.
متن کاملEssential Localizations and Infinitary Exact Completion
We prove the universal property of the infinitary exact completion of a category with weak small limits. As an application, we slightly weaken the conditions characterizing essential localizations of varieties (in particular, of module categories) and of presheaf categories. Introduction An essential localization is a reflective subcategory such that the reflector has a left adjoint. In [12], R...
متن کاملA Note on the Exact Completion of a Regularcategory , and Its
A new description of the exact completion C ex/reg of a regular category C is given, using a certain topos Shv(C) of sheaves on C; the exact completion is then constructed as the closure of C in Shv(C) under nite limits and coequalizers of equivalence relations. An innnitary generalization is proved, and the classical description of the exact completion is derived.
متن کاملExact completions and toposes
Toposes and quasi-toposes have been shown to be useful in mathematics, logic and computer science. Because of this, it is important to understand the different ways in which they can be constructed. Realizability toposes and presheaf toposes are two important classes of toposes. All of the former and many of the latter arise by adding “good” quotients of equivalence relations to a simple catego...
متن کاملA note on Cauchy completeness for preorders
In this paper, we study the notion of Cauchy-complete preorder in a regular category, following work in [CS86], introducing the logic of a regular category. We give a different, stronger characterization than in loc.cit. for those preorders. Using this, we provide a new construction of the Cauchy-completion in a exact category. AMS Classification: 18A40, 03G30.
متن کامل