categories: Preprint "The Syntax of Coherence"

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

The preprint

"The Syntax of Coherence"

is available on
http://xxx.lanl.gov/abs/math.CT/9910006

Abstract: This article tackles categorical coherence within a two-dimensional
generalization of Lawvere's functorial semantics. 2-theories, a syntactical
way of describing categories with structure, are presented. From the
perspective here afforded, many coherence results become simple 
statements about the quasi-Yoneda lemma and 2-theory-morphisms.
Given two 2-theories and a 2-theory-morphism between them, we 
explore the induced relationship between the corresponding 2-categories
of algebras. The strength of the induced quasi-adjoints are classified 
by the strength of the 2-theory-morphism. These quasi-adjoints reflect
the extent to which one structure can be replaced by another.
A two-dimensional analogue of the Kronecker product is defined 
and constructed. This operation allows one to generate new coherence 
laws from old ones. 


All the best, 
Noson S. Yanofsky