Affiliation:

Aix-Marseille Université

Date:

Mon, 13/02/2017 - 14:00 - 15:00
The category n-Cat of strict n-categories and strict n-functors is endowed with

a rich structure that is only partially understood. First, it is endowed with a tensor

product, generalizing Gray's tensor product of 2-categories, first defined by Al-Alg

and Steiner in the early 90's. This implies that n-Cat, endowed with lax transformations

and higher lax transformations, form an n-Gray-category in some appropriate sense.

Second, it is endowed with a join construction, generalizing the join construction of

categories and compatible with the one of simplicial sets, defined recently by myself

and Georges Maltsiniotis. This join is related by adjunctions to slices. The interaction

between the tensor product and the join is described by conjectures. These conjectures

are still open but a small part of them that we managed to prove easily implies a Quillen's

Theorem A for strict n-categories, which was the original motivation for the introduction

of the join.