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

on locally presentable and accessible categories. There is a

made available by the authors.


  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

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.

A\phantom{A}(n,r)-categoriesA\phantom{A}A\phantom{A}toposesA\phantom{A}locally presentableloc finitely preslocalization theoremfree cocompletionaccessible
(0,1)-category theorylocalessuplatticealgebraic latticesPorst’s theorempowersetposet
category theorytoposeslocally presentable categorieslocally finitely presentable categoriesAdámek-Rosický‘s theorempresheaf categoryaccessible categories
model category theorymodel toposescombinatorial model categoriesDugger's theoremglobal model structures on simplicial presheavesn/a
(∞,1)-category theory(∞,1)-toposeslocally presentable (∞,1)-categoriesSimpson’s theorem(∞,1)-presheaf (∞,1)-categoriesaccessible (∞,1)-categories
category: reference

Last revised on March 1, 2019 at 17:09:39. See the history of this page for a list of all contributions to it.