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.


  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 July 6, 2018 at 08:13:40. See the history of this page for a list of all contributions to it.