Theorem 2.5. A category E E is equivalent to a presheaf topos if and only if it is cocomplete, well-powered, co-well-powered, atomic, and regular.

A locally small category embeds fully and faithfully into the category of set-valued presheaves via the Yoneda embedding which to every object of associates ...

9 окт. 2021 г. · An important class of presheaves is those on a category of open subsets Op ( X ) Op(X) of a topological space or smooth manifold X X .

Similarly, we can define the notion of a presheaf of abelian groups, rings, etc. More generally we may define a presheaf with values in a category.

17 нояб. 2019 г. · I am trying to understand categories of presheaves, starting from a somewhat hazy understanding of presheaves. Limits and colimits in the category of presheaves An equivalence of categories of presheaves. Другие результаты с сайта math.stackexchange.com

24 мар. 2011 г. · The category of presheaves Pre(C) on a small category C is the category of functors Cop→Sets. Since the category of sets is co-complete and ...

4.36 Presheaves of categories. In this section we compare the notion of fibred categories with the closely related notion of a “presheaf of categories”.

14 дек. 2015 г. · Given a category C, the category of presheaves ˆC is the category of functors Cop → Set and natural transfor- mations between them. 1 ...

Introduction. Our goal is to define the Yoneda embedding for ∞-categories and prove that it satisfies a universal property.

28 дек. 2021 г. · We say that a category is algebraically complete when every endofunctor has an initial algebra. Similarly, a category is algebraically ...