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.

3 окт. 2012 г. · Small (co)complete categories are posets by a theorem of Freyd. If C has all small coproducts and its class of morphisms C1 is small, ...

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.

26 дек. 2022 г. · Thus I want to construct K_0 as a functor from the category of essentially U-small abelian categories to the category of U-small abelian groups.

25 янв. 2023 г. · We assume ZFC+U. A category is an ordered pair (ObC,MorC,dom,codom,e,∘) of sets (not classes) and maps satifying some conditions.

30 окт. 2009 г. · Everybody agrees that a U-small category is a category whose sets of objects and morphisms are both elements of U.

12 янв. 2018 г. · So, a total selection is a way to pick exactly one morphism in every non-empty Hom-set of C, while being compatible with the category structure.

9 янв. 2010 г. · The correct statement is: A small category is accessible if and only if it is idempotent complete. This is proved (I think) in Adamek & Rosicki, Locally ...

3 окт. 2012 г. · All the standard examples for model categories are large categories. Is it possible to have a small model category? Are there any interesting examples?

12 янв. 2023 г. · Freyd's theorem in classical category theory says that any small category C admitting products indexed by the set C1 of all its arrows is a ...