Thanks for these comments. I was mainly investigating the acceptance of these terms by the categorical community, to decide if I should change for the new edition of my old book. I agree with Paul's comments to me personally that it is a good idea to avoid overworked terms (like `universal'). The issue is that for a morphism f: G \to H of groupoids, the notion of quotient introduced by Philip Higgins, namely if f is full and Ob(f) is surjective, is fine. The other important notion is that f comes from an identification of objects, which in Paul's terminology would be supine (w.r.t. the opfibration Ob: Gpds \to Sets). More vivid would be H is a 0-identification of G, that is the groupoid H is then obtained from G by an identification of objects. It would tie in with other situations to say that H is induced from G by Ob(f). There is a good case for not introducing new words. Ronnie ----- Original Message ----- From: "Prof. Peter Johnstone" <P.T.Johnstone@dpmms.cam.ac.uk> To: "Ronald Brown" <ronnie@ll319dg.fsnet.co.uk> Cc: <categories@mta.ca> Sent: Wednesday, December 07, 2005 9:05 AM Subject: Re: categories: Terminology question wrt fibrations of categories.
On Tue, 6 Dec 2005, Ronald Brown wrote:
on the other hand Paul Taylor, following Peter Johnstone, I understand, uses \phi is prone, supine, instead of cartesian, cocartesian
`Prone' and `supine' were invented by Paul Taylor; I copied them from him, not the other way round. I'm sorry Ronnie doesn't like them; they seem to me a very neat way of finding two words that both mean `lying horizontally' but have an opposite handedness about them.
Peter Johnstone