Preprint: Coherence, Homotopy and 2-Theories

Preprint: Coherence, Homotopy and 2-Theories

[Noson Yanofsky]

The following preprint is available on the xxx.lanl.gov archive:

http://xxx.lanl.gov/abs/math.CT/0007033

Coherence, Homotopy and 2-Theories
Authors: Noson S. Yanofsky
Comments: 32 pages; XY-Pic
Subj-class: Category Theory; Quantum Algebra
MSC-class: 18D10; 18C10; 55U35

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. 



All the best, 
Noson