Dear Steve, A bicomma object is a bicategorical limit, so determined only up to equivalence. A comma object is a strict limit, so determined up to isomorphism. In the case of Cat, comma objects are just the usual comma categories (strictly speaking, anything isomorphic to the comma category), while anything equivalent to the comma category will be a bicomma object. So any comma object is also a bicomma object, but the converse is false. Moreover, there are 2-categories in which bicomma objects exist but comma objects do not. The situation with pullbacks, by the way, is slightly different. It is not the case that every pullback is a bipullback (but there is a paper of Joyal and Street giving a sufficient condition for a pullback to be a bipullback). Steve. -----Original Message----- From: cat-dist@mta.ca on behalf of Steve Vickers Sent: Wed 25/07/2007 2:02 AM To: categories@mta.ca Subject: categories: Bicomma objects What is the difference between a bicomma object and a comma object (a.k.a. lax pullback)? Steve.