hide
Free keywords:
Mathematics, Category Theory, Algebraic Topology
Abstract:
In this article we extend the theory of lax monoidal structures, also known
as multitensors, and the monads on categories of enriched graphs that they give
rise to. Our first principal result -- the lifting theorem for multitensors --
enables us to see the Gray tensor product of 2-categories and the Crans tensor
product of Gray categories as part of this framework. We define weak
n-categories with strict units by means of a notion of reduced higher operad,
using the theory of algebraic weak factorisation systems. Our second principal
result is to establish a lax tensor product on the category of weak
n-categories with strict units, so that enriched categories with respect to
this tensor product are exactly weak (n+1)-categories with strict units.
