2-operads and bicategories
Michael Batanin (04/09/96)
I consider in this talk the two dimensional case of the general definition
of a weak omega-category (this definition was given in my talks on 14
August 1996 at Macquarie University ) My aim is to demonstrate that the
weak 2-categories in the sense of this general definition are bicategories
and conversely.
For this I investigate thoroughly the structure of contractible 2-operads
and prove the following lemma
Lemma. The category of pointed contractible 2-operads is isomorphic to the
category of pointed nonsymmetric chaotic Cat-operads (where chaotic means
that an operad consists of chaotic categories) and hence, to the category
of pointed
nonsymmetric Set-operads.
This lemma allows to prove the following proposition.
Proposition. Every algebra over a contractible pointed 2-operad may be
endowed with a canonical sructure of a bicategory. Conversely, every
bicategory has a canonical structure over the universal pointed
contractible 2-operad.
The proof uses the coherence theorem for bicategories.
Other talks by the same speaker.
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Steve Lack
Last modified: Tue May 19 13:58:38 EST 1998
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