2 November 2004
2:30 - 3:45   Joachim Kock

On the notion of unit in monoidal categories and monoidal 2-categories

Abstract:
(This is joint work with Andri Joyal.)
First I will explain how the notion of unit in a monoidal category can be
formulated in terms of cancellative idempotents.  This formulation does not
involve left or right constraints, and it is independent of associativity
of the tensor.  Then I will illustrate how this approach is well-suited
to higher dimensional generalisation, by working out the case of monoidal
2-categories, comparing with the notion of unit coming from tricategories.
Finally I will outline the proof of the basic result that the category of
cancellative idempotents is contractible.  This means that up to homotopy
'being unital' is a property, although introduced as a structure.