From: "Hans-E. Porst" <porst@uni-bremen.de>
To: categories@mta.ca,
Subject: Re: Terminology re fibrations and opfibrations of categories
Date: Mon, 2 Jan 2006 17:20:57 +0100 [thread overview]
Message-ID: <B3396291-A4B2-4814-8531-C3F7422A83AF@uni-bremen.de> (raw)
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 porst@uni-bremen.de
Bremen, Germany Fax: +49-421-75643
next reply other threads:[~2006-01-02 16:20 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2006-01-02 16:20 Hans-E. Porst [this message]
-- strict thread matches above, loose matches on Subject: below --
2005-12-22 8:07 Ronald Brown
2005-12-26 21:57 ` Eduardo Dubuc
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