Weak n-categories with strict units via iterated enrichment

Mark Weber – 4 July 2012, 11 July 2012, 18 July 2012, 27 July 2012

It's well-known that strict n-categories have an easy inductive definition via iterated enrichment:

Strict-(n+1)-Cat = (Strict-n-Cat, x)-Cat.

In this talk the operads for weak n-categories with strict units will be described, and from them the theory of multitensors will be used to construct a "tensor product" T(n) on the category W(n) of weak n-categories with strict units, giving a similar inductive formulation for such structures:

W(n+1) = (W(n),T(n))-Cat.