Subject: categories: Re: Terminology re fibrations and opfibrations of categories

From: "Hans-E. Porst" <[email-masked]>
Date: Mon, 2 Jan 2006 17:20:57 +0100

Note that the suggestion below is standard terminology since about 30
years. See also

Adamek, Herrlich, Strecker: Abstract and concrete categories; Wiley 1990
(also available at   http://katmat.math.uni-bremen.de)

H.-E. Porst

Am 26.12.2005 um 22:57 schrieb Eduardo Dubuc:

> I am just writing a paper with Luis Espannol where we need to
> develop (the
> basic part of the theory of cartesian and cocartesian arrows) for
> families
>
> we use the following terminology:
>
> consider a functor  U: C ---> S, then:
>
> 1)  a family in C              Z _i ---> X
>
> over                           R_i --->  S   is    FINAL   iff:
>
> given   S ---> T = UY  such that there exists   Z_i --->Y   over
> R_i ---> S ---> T (that is,  R_i ---> S ---> T lifts), then there
> exists a
> unique   X ---> Y over   S ---> T (that is,  S ---> T lifts).
>
> For topological spaces this is the usual Bourbaki notion of final
> topology.
>
> When U is not understood, we call this  "U-FINAL"

--
Hans-E. Porst                                      [email-masked]
Bremen, Germany                                     Fax: +49-421-75643