Subject: question to topology list re category Date: Wed, 13 Mar 2002 09:07:53 -0600 From: David Yetter Joan Birman forwarded to me the question posed by James Cruickshank to the topology list. I have not seen the specific category you asked about before, but in general if one has a category C with (chosen) pushouts for all pairs of maps with a common source, the category with diagrams of the form X----> M <------Y as arrows, and composition given by pushout is called the category of cospans in C. (For some reason it has been more common among categorists to consider the dual notion-- the category of spans in a category with pullbacks.) Best Thoughts, David Yetter