In mathematics, especially

category theory Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory ...

, an (∞, ''n'')-category is a generalization of an

∞-category In mathematics, more specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex, quategory) is a generalization of the notion of a Category (ma ...

, where each ''k''-morphism is invertible for

k > n

. Thus, an ∞-category is an (∞, 1)-category, while an

∞-groupoid In category theory, a branch of mathematics, an ∞-groupoid is an abstract homotopical model for topological spaces. One model uses Kan complexes which are fibrant objects in the category (mathematics), category of simplicial sets (with the standa ...

is an (∞, 0)-category.

References

*nlab
(infinity,n)-category in nLab
*

See also

References

Further reading