Quasi-category

Definition

In mathematics, more specifically category theory, a quasi-category is a generalization of the notion of a category. The study of such generalizations is known as higher category theory.

Related concepts

(∞, n)-category 2-functor 2-group 2-ring 3-category Abelian category Accessible ∞-category Additive category Adjoint functors Advances in Mathematics Algebraic category André Joyal Anodyne extension Bicategory Cambridge University Press Cartesian closed category Cartesian fibration Categorification Category (mathematics)Category of abelian groups Category of groups Category of magmas Category of modules Category of relations Category of rings Category of sets Category theory Coequalizer Cokernel Colimit Combinatorial model category Comma category Commutative diagram Complete category Concrete category Cone (category theory)Conservative functor Coproduct Core of a category Core of an ∞-category Denis-Charles Cisinski Derived functor Diagonal functor Diagram (category theory)Direct limit En-ring End (category theory)Enriched category Epimorphism Equaliser (mathematics)Equivalence of categories Essentially surjective functor Exact functor Exponential object Final object Forgetful functor Free category Full and faithful functors Functor Functor category Fundamental group Globular set Glossary of category theory Grothendieck construction Higher-dimensional algebra Higher Topos Theory Higher category theory Homotopy category Homotopy category of an ∞-category Homotopy coherent nerve Homotopy hypothesis Initial and terminal objects Inverse limit Isomorphism Isomorphism of categories Jacob Lurie Joyal fibration Julie Bergner Kan (mathematics)Kan complex Kan extension Kan fibration Kernel (category theory)Kleisli category Limit (category theory)Limits and colimits in an ∞-category Localization of a category Localization of an ∞-category Mackey functor Model category Monoidal category Monoidal functor Monomorphism Morphism N-group (category theory)N-monoid NLab Natural transformation Nerve functor Nerve of a category Opposite category Outline of category theory Overcategory Pre-abelian category Preadditive category Princeton University Press Product (category theory)Product category Pseudo-functor Pullback (category theory)Pushout (category theory)Quillen adjunction Quotient category Representable functor Segal category Segal space Simplex category Simplicial set Simplicially-enriched category Simplicially enriched category Smooth functor Springer-Verlag Stable infinity category Stable ∞-category Straightening (category theory)Strict 2-category Strict n-category String diagram Subcategory Symmetric monoidal category Tetracategory Topological category Topos Traced monoidal category Tricategory Universal construction Universal property Weak equivalence between simplicial sets Weak n-category Yoneda lemma Zero morphism ∞-Yoneda embedding ∞-category of Kan complexes ∞-groupoid ∞-topos

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