How to generate G-topologies for module presheaf categories
نویسنده
چکیده
respectively. We refer to one of these as the parent category, with R or C as the indexing gadget. From a categorical perspective the different kinds of parent categories have a lot in common. We could say that Mod -R is just an additive version of Ĉ . That is a bit too glib, but the analysis of the two kinds of categories is quite similar. For each parent category there is a notion of a localization, a certain kind of quotient of the category (although in the Ĉ case this is usually described as a subcategory). In both cases each localization is determined by, and determines, a
منابع مشابه
Exact 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 کاملQuasi-varieties of presheaves
In analogy with the varietal case, we give an abstract characterization of those categories occurring as regular epireflective subcategories of presheaf categories such that the inclusion functor preserves small sums. MSC 2000 : 18A40, 18F20. The aim of this short note is to add one step to the nice parallelism between presheaf categories and algebraic categories. Presheaf categories can be abs...
متن کاملClosure Operators in Exact Completions
In analogy with the relation between closure operators in presheaf toposes and Grothendieck topologies, we identify the structure in a category with finite limits that corresponds to universal closure operators in its regular and exact completions. The study of separated objects in exact completions will then allow us to give conceptual proofs of local cartesian closure of different categories ...
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 کاملPresheaf Models for Concurrency
In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for ...
متن کامل