Locally presentable category
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The general idea is that a locally presentable category is a large category generated from small data: from small objects under small colimits. Presentation by combinatorial model categories.Locally presentable ( ∞, 1 ) (\infty,1)-categories.Localizations of ( ∞, 1 ) (\infty,1)-categories.Basic idea in ( ∞, 1 ) (\infty,1)-category theory.Model structure on simplicial presheaves.
#Locally presentable category free
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Model structure on differential-graded commutative algebras
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On modules over an algebra over an operad On simplicial T-algebras, on homotopy T-algebras Model structure on reduced simplicial sets Model structure on equivariant dgc-algebras Model structure on equivariant chain complexes Model structure on cosimplicial simplicial setsįine model structure on topological G-spacesĬoarse model structure on topological G-spacesįor rational equivariant ∞ \infty-groupoids On chain complexes/ model structure on cosimplicial abelian groups On simplicial sets, on semi-simplicial sets Model structure on presheaves over a test category The first chapter is devoted to an important class of categories, the locally presentable categories, which is broad enough to encompass a great deal of. Presentation of ( ∞, 1 ) (\infty,1)-categories Grothendieck construction for model categories Where locally presentable categories are called just presentable categories.( relative category, homotopical category)Ĭartesian closed model category, locally cartesian closed model category This says equivalently that a locally presentable category ? \mathcal-presentable categories ( pdf)įrancis Borceux, Handbook of Categorical Algebra: III Categories of Sheaves (proposition 3.4.16), page 220. Locally finitely presentable categoriesĪ locally presentable category is a category which contains a small set S S of small objects such that every object is a nice colimit over objects in this set.Well-poweredness and well-copoweredness.Stability of presentability under various operations.Finite presentability and Gabriel–Ulmer duality.As localizations of presheaf categories.