nLab
locally presentable categories - table
Locally presentable categories: Large categories whose objects arise from small generators under small relations.
| (n,r)-categories… | satisfying Giraud's axioms | inclusion of left exaxt localizations | generated under colimits from small objects | | localization of free cocompletion | | generated under filtered colimits from small objects |
|---|
| (0,1)-category theory | (0,1)-toposes | | algebraic lattices | Porst’s theorem | subobject lattices in accessible reflective subcategories of presheaf categories | | |
| category theory | toposes | | locally presentable categories | Adámek-Rosický’s theorem | accessible reflective subcategories of presheaf categories | | accessible categories |
| model category theory | model toposes | | combinatorial model categories | Dugger’s theorem | left Bousfield localization of global model structures on simplicial presheaves | | |
| (∞,1)-topos theory | (∞,1)-toposes | | locally presentable (∞,1)-categories | Simpson’s theorem | accessible reflective sub-(∞,1)-categories of (∞,1)-presheaf (∞,1)-categories | | accessible (∞,1)-categories |
Revised on October 17, 2012 12:31:38
by
Urs Schreiber
(82.169.65.155)