nLab
Locally Presentable and Accessible Categories

Locally Presentable and Accessible Categories is a book by Jiří Adámek and Jiří Rosický about, unsurprisingly, locally presentable and accessible categories. It was published by Cambridge University Press in the London Mathematical Society Lecture Note Series, number 189, in 1994.

Content

  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 localizations of free cocompletions. Accessible categories omit the cocompleteness requirement; toposes add the requirement of a left exact localization.

(n,r)-categoriestoposeslocally 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)-topos theory(∞,1)-toposeslocally presentable (∞,1)-categoriesSimpson’s theorem(∞,1)-presheaf (∞,1)-categoriesaccessible (∞,1)-categories

category: reference

Revised on March 5, 2015 12:14:36 by Urs Schreiber (195.113.30.252)