Re: Terminology question wrt fibrations of categories.

["Ronald Brown" <ronnie@ll319dg.fsnet.co.uk>]

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
>
>
>