nLab
Locally Presentable and Accessible Categories

This page collects material related to the book

• 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

on locally presentable and accessible categories. There is a

• list of corrections

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	Adámek-Rosický‘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