nLab
PrCat

Context

Category theory

Concepts

Universal constructions

    • /

    • /

Theorems

Extensions

Applications

Compact objects

objects dCd \in C such that C(d,)C(d,-) commutes with certain

    • ,

Models

Relative version

Contents

Idea

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 PrCatPrCat whose objects are locally presentable categories, and whose morphisms are left adjoint functors.

The analog of this

Locally presentable categories: possibly- generated under by under . Equivalently, of . Accessible categories omit the cocompleteness requirement; toposes add the requirement of a localization.

A\phantom{A}A\phantom{A}A\phantom{A}A\phantom{A}locally presentableloc finitely preslocalization theoremaccessible
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.