Towards a Thomason model structure on strict $n$-categories

The homotopy theory of small categories was mainly founded by Quillen in his quest for a definition of higher algebraic K-theory. Quillen in particular showed his famous theorems A and B, and the fact that the homotopy category of small categories (endowed with the weak equivalences induced by the nerve functor) is equivalent to the homotopy category of spaces. This equivalence of homotopy categories was then promoted to a Quillen equivalence by Thomason.

In this talk based on joint work with Georges Maltsiniotis, I will present some ideas on the homotopy theory of strict n-categories. In particular, I will explain a conditional proof of the existence of a Thomason model structure on strict n-categories. For n = 1 and n = 2, we will deduce this existence unconditionally.