Workshop on Categorical Methods in Algebra, Geometry and 
Mathematical Physics (StreetFest), Canberra,July 18-21 2005.

Speaker: Joachim Kock (Universitat Aut˜noma de Barcelona)

Title: Weak units and homotopy 3-types

Abstract:

Joint work with A. Joyal.

It is shown that every braided monoidal category arises as End(I) 
for a weak unit I in an otherwise completely strict monoidal 
2-category.  This implies a version of Simpson's weak-unit 
conjecture in dimension 3, namely that one-object 3-groupoids 
that are strict in all respects, except that the object has only 
weak identity arrows, can model all simply connected homotopy 
3-types. The proof has a clear conceptual content and relies on 
a geometrical argument with string diagrams and configurations 
spaces.