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.


  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: Large categories whose objects arise from small generators under small relations.

(n,r)-categoriessatisfying Giraud's axiomsinclusion of left exact localizationsgenerated under colimits from small objectslocalization of free cocompletiongenerated under filtered colimits from small objects
(0,1)-category theory(0,1)-toposes\hookrightarrowalgebraic lattices\simeq Porst’s theoremsubobject lattices in accessible reflective subcategories of presheaf categories
category theorytoposes\hookrightarrowlocally presentable categories\simeq Adámek-Rosický’s theoremaccessible reflective subcategories of presheaf categories\hookrightarrowaccessible categories
model category theorymodel toposes\hookrightarrowcombinatorial model categories\simeq Dugger’s theoremleft Bousfield localization of global model structures on simplicial presheaves
(∞,1)-topos theory(∞,1)-toposes\hookrightarrowlocally presentable (∞,1)-categories\simeq
Simpson’s theorem
accessible reflective sub-(∞,1)-categories of (∞,1)-presheaf (∞,1)-categories\hookrightarrowaccessible (∞,1)-categories

category: reference

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