Unifying exact completions
نویسندگان
چکیده
We define the notion of exact completion with respect to an existential elementary doctrine. We observe that the forgetful functor from the 2-category exact categories to existential elementary doctrines has a left biadjoint that can be obtained as a composite of two others. Finally, we conclude how this notion encompasses both that of the exact completion of a regular category as well as that of the exact completion of a cartesian category with weak pullbacks. MSC 2000: 03G30 03B15 18C50 03B20 03F55
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 کاملCocomplete toposes whose exact completions are toposes
Let E be a cocomplete topos. We show that if the exact completion of E is a topos then every indecomposable object in E is an atom. As a corollary we characterize the locally connected Grothendieck toposes whose exact completions are toposes. This result strengthens both the Lawvere–Schanuel characterization of Boolean presheaf toposes and Hofstra’s characterization of the locally connected Gro...
متن کاملA Characterization of the Left Exact Categories Whose Exact Completions Are Toposes
We characterize the categories with finite limits whose exact completions are toposes. We review the examples in the literature and also find new examples and counterexamples.
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 کاملA 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Categorical Structures
دوره 23 شماره
صفحات -
تاریخ انتشار 2015