nLab Locally Presentable and Accessible Categories

This page is to record the reference:

• Jiří Adámek, Jiří Rosický:

  
  

  Locally Presentable and Accessible Categories

  
  

  London Mathematical Society Lecture Note Series, number 189,

  Cambridge University Press 1994

  doi:10.1017/CBO9780511600579

  erratum: pdf

on locally presentable and accessible categories. There is an erratum made available by the authors:

Contents

1. locally presentable categories

2. accessible categories: see also sketch

3. algebraic categories: see algebraic category, equationally presentable category, essentially algebraic theory, and variety of algebras

4. injectivity class?es: see also weak factorization system

5. categories of models: see internal logic, theory, essentially algebraic theory, model

6. Vopěnka's principle

• Appendix: large cardinals

Related concepts

Locally presentable categories: Cocomplete possibly-large categories generated under filtered colimits by small generators under small relations. Equivalently, accessible reflective localizations of free cocompletions. Accessible categories omit the cocompleteness requirement; toposes add the requirement of a left exact localization.

$\phantom{A}$(n,r)-categories$\phantom{A}$	$\phantom{A}$toposes$\phantom{A}$	locally presentable	loc finitely pres	localization theorem	free cocompletion	accessible
(0,1)-category theory	locales	suplattice	algebraic lattices	Porst’s theorem	powerset	poset
category theory	toposes	locally presentable categories	locally finitely presentable categories	Gabriel–Ulmer’s theorem	presheaf category	accessible categories
model category theory	model toposes	combinatorial model categories		Dugger's theorem	global model structures on simplicial presheaves	n/a
(∞,1)-category theory	(∞,1)-toposes	locally presentable (∞,1)-categories		Simpson’s theorem	(∞,1)-presheaf (∞,1)-categories	accessible (∞,1)-categories

category: reference