objects $d \in C$ such that $C(d,-)$ commutes with certain
,
When working with locally presentable categories, one is typically interested only in the colimit-preserving functors between them, hence (by the adjoint functor theorem) equivalently the left adjoint functors.
One hence considers the very large category $PrCat$ whose objects are locally presentable categories, and whose morphisms are left adjoint functors.
The analog of this
in (∞,1)-category theory is Pr(∞,1)Cat;
in model category-theory is Ho(CombModCat).
Locally presentable categories: possibly- generated under by under . Equivalently, of . Accessible categories omit the cocompleteness requirement; toposes add the requirement of a localization.
$\phantom{A}$$\phantom{A}$ | $\phantom{A}$$\phantom{A}$ | locally presentable | loc finitely pres | localization theorem | accessible | |
---|---|---|---|---|---|---|
Porst’s theorem | ||||||
Adámek-Rosický‘s theorem | ||||||
global | n/a | |||||
Simpson’s theorem |
Created on July 6, 2018 at 15:49:04. See the history of this page for a list of all contributions to it.