Re: Higher Lawvere theories?

["Noson S. Yanofsky" <noson@sci.brooklyn.cuny.edu>]

Hi,

In a paper:
Coherence, Homotopy and 2-Theories
K-Theory 23: Pgs 203 - 235. (2001).
I worked out much of 2-Theories and their relationship with coherence
theory.

Abstract:
2-Theories are a canonical way of describing categories with extra
structure. 2-theory-morphisms are used when discussing how one structure can
be replaced with another structure. This is central to categorical coherence
theory. We place a Quillen model category structure on the category of
2-theories and 2-theory-morphisms where the weak equivalences are
biequivalences of 2-theories. A biequivalence of 2-theories (Morita
equivalence) induces and is induced by a biequivalence of 2-categories of
algebras. This model category structure allows one to talk of the homotopy
of 2-theories and discuss the universal properties of coherence.

There is also a version on the arXiv:
http://xxx.lanl.gov/abs/math.CT/0007033

All the best,
Noson Yanofsky
-----Original Message-----
From: Mike Stay [mailto:metaweta@gmail.com]
Sent: Friday, August 02, 2013 12:35 PM
To: categories
Subject: categories: Higher Lawvere theories?

Has anyone worked out the details of "higher Lawvere theories" so that one
can say "the free bicategory on this object, these morphisms, these
2-morphisms, modulo these equations of 2-morphisms"?
--
Mike Stay - metaweta@gmail.com
http://www.cs.auckland.ac.nz/~mike
http://reperiendi.wordpress.com



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