On Fri, May 27, 2011 at 10:16 AM, Finn Lawler <flawler@cs.tcd.ie> wrote:
Mike Stay wrote:
Has anyone "unpacked" the meaning of the Gray tensor product of strict 2-categories? I'm looking for something like "the Gray product C tensor D is the 2-category whose - objects are pairs (c,d) - morphisms are ... - 2-morphisms are ..."
Gray's book Formal Category Theory: Adjointness for 2-Categories (Springer LNM 391) is the original reference. Theorem 4.9 constructs the 'lax' tensor product. A good reference for the 'pseudo' tensor product is chapter 5 of Nick Gurski's 2007 Ph.D. thesis 'An algebraic theory of tricategories'.
Thanks to everyone! Gurski's exposition is exactly what I was looking for. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]