Quasi-categories live at the intersection of homotopy theory with category theory. In particular, they serve as a model for (∞, 1)-categories, that is, weak higher categories with n-cells for each natural number n that are invertible when n > 1. Alternatively, an (∞, 1)-category is a category enriched in ∞-groupoids, e.g., a topological space with points as 0-cells, paths as 1-cells, homotopies...

One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt the machinery of globular operads [4] to this task. The resulting theory includes the Gray tensor product of 2-categories and the Crans tensor product [12] of Gray categories. Moreover much of the pre...

We prove general adjoint functor theorems for weakly (co)complete $n$-categories. This class of $n$-categories includes the homotopy $\infty$-categories -- in particular, these do not admit all small (co)limits general. also introduce Brown representability (homotopy) and a theorem localizations compactly generated presentable if $n \geq 2$ stable any 1$.