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.

24 июн. 2012 г. · Any category of algebraic structures will be large (because there is always at least one model, and there is a proper class of sets of any given ...

11 авг. 2010 г. · To be clear, a category is small if its class of objects is a set. A category is sometimes called locally small if for every pair of objects A,B ...

2 нояб. 2023 г. · Perhaps the most fundamental example of a small category in topology is the simplex category Δ. The objects are non-empty finite linear orders, ...

20 июн. 2021 г. · Many categories in practice are not small, but they are locally small. But in order to formalize this, it is best to assume another Grothendieck ...

10 февр. 2023 г. · "A category is said to be essentially small if it is equivalent to a small category. Assuming the axiom of choice, this is the same as saying ...

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.

9 июл. 2019 г. · A category is called small if the collections of objects and of all the morphisms between objects are sets. If only the latter is true, a ...

4 мая 2018 г. · 1 Answer 1 · The small universe consists of sets · The large universe consists of the (first-order) unary predicates (with parameters) you can ...

11 июл. 2019 г. · No, elements of Cat are small categories - Cat×Cat is the domain, and Cat the codomain, of ×. Analogously, "a function on natural numbers" ...