6 июл. 2024 г. · Definition. A category is small if it has a small set of objects and a small set of morphisms. In other words, a small category is an ...

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

28 окт. 2016 г. · A category C is called small if both the collection of objects and arrows are sets. Otherwise the category is called large. Examples of small categories - Mathematics Stack Exchange Essentially small categories and skeletal categories Другие результаты с сайта math.stackexchange.com

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.

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. (Some authors assume this ...

Noun. small category (plural small categories) (category theory) A category such that all of its objects form a set and all of its morphisms form a set.

A directed graph. Any directed graph generates a small category: the objects are the vertices of the graph, and the morphisms are the paths in the graph ( ...

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 ...

28 дек. 2011 г. · As Mike says, it's locally finitely presentable because Cat is (equivalent to) the category of models of a finite limit sketch. Small categories and completeness - MathOverflow What's a reasonable category that is not locally small? Why do we care about small sets? - MathOverflow On the definition of small categories in SGA4 - MathOverflow Другие результаты с сайта mathoverflow.net

Definition 1.2. We say a category C is small if it has only a set of objects and a set of morphisms.