25 апр. 2020 г. · Definition. A category is said to be locally small if each of its hom-sets is a small set, i.e., is a set instead of a proper class.

A locally small category is a category whose hom-sets are (small) sets. More explicitly, it is a category such that for all objects and in the category, there ...

24 июл. 2017 г. · A category C is small if Obj(C)∈U, and large otherwise. Morever, C is locally small if for each A,B∈Obj(C), we have Hom(A,B)∈U. Why do we care about locally small categories (as opposed to ... On the notion of (locally) small categories - Math Stack Exchange Другие результаты с сайта math.stackexchange.com

Redirect to: Category (mathematics)#Small and large categories · Last edited on 22 October 2022, at 10:32. Languages. This page is not available in other ...

29 окт. 2009 г. · A category C is locally small if the class of morphisms between any two of its objects is a set. Of course, a small category is necessarily locally small. How should we define "locally small"? - MathOverflow Is the category of small categories locally presentable? How should one call and use categories that are not locally ... is the presheaf category of a locally small category locally small? Другие результаты с сайта mathoverflow.net

6 июл. 2024 г. · A small category structure on a locally small category C is an essentially surjective functor from a set (as a discrete category) to C . A ...

25 авг. 2015 г. · A category is locally small if for each pair of its objects, A and B , the maps A→B A → B form a set, not a proper class.

3 авг. 2021 г. · Definition. Let C be a metacategory. Then C is said to be locally small if and only if all of its hom classes are sets.

5 окт. 2017 г. · A category is called locally small if, for any pair of objects A and B, the class of morphisms from A to B is a set.

The category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms are functors between categories.