On Sat, 11 Sep 2010, David Leduc wrote:
In a bicategory, composition of 1-cells is associative up to isomorphism. Because it would be evil to insist that h o (g o f) is equal to (h o g) o f. However the source and target objects of those compositions must be equal. Isn't it evil? Why not weaken this requirement by saying that the sources (respectively, targets) of h o (g o f) and (h o g) o f must only be isomorphic?
Your question made me wonder why the axioms for ordinary categories, i.e. 1-categories, insist that in composing f:A->B and g:C->D, B and C must be equal. Isn't it just as evil not to allow them to be merely isomorphic? Jocelyn Paine http://www.j-paine.org Jocelyn's Cartoons: http://www.j-paine.org/blog/jocelyns_cartoons/ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]