Joachim Kock

Title:  Weak units and realisation of homotopy 3-types

Abstract:  First I'll outline a general approach to higher categories
with strict composition laws but only weak identity cells.  The approach
is simplicial in spirit, but the base category is a certain category of
'coloured ordinals' instead of the usual Delta.  Then I'll restrict
attention to the one-object case of dimension 3, and explain how strict
2-categories with a strict tensor product and weak units can realise
connected, simply connected homotopy 3-types.   This example is the
first step towards Simpson's conjecture that every weak n-category is
equivalent to one with strict composition laws (but weak identity
cells).