From: "Fred E.J. Linton" <fejlinton@usa.net>
To: claudio pisani <pisclau@yahoo.it>, <categories@mta.ca>
Subject: Re: question on terminology
Date: Fri, 24 Aug 2012 23:35:10 -0400 [thread overview]
Message-ID: <E1T5Fg8-0007CN-3z@mlist.mta.ca> (raw)
Claudio Pisani asked,
> Is there a standard name for those presheaves X on a
> category C such that Xf is a bijection for any f in C?
Well, those presheaves are exactly the "restrictions to C" of the
presheaves on the grouppoid reflection (the grouppoidal 'quotient') of C
(by which I mean the category got by declaring invertible every C-morphism).
Does that suggest "grouppoidal action of C" might work? I think I'd tend
to lobby against the use of the prefix "bi-" unless there were *really*
compelling reasons in favor of it.
Cheers, -- Fred
---
> I have sometimes called them "biactions" since any such X (considered as,
say, a left action of C) is paired with the obvious presheaf X' on C^op (a
right action of C): X'f = (Xf)^-1.
> Of course, they correspond, as categories over C, to discrete bifibrations.
> I also know that the separable or decidable presheaves are those for which
every Xf is injective.
>
> Claudio
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2012-08-25 3:35 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2012-08-25 3:35 Fred E.J. Linton [this message]
2012-08-25 13:16 ` Colin McLarty
-- strict thread matches above, loose matches on Subject: below --
2012-08-26 4:59 Fred E.J. Linton
[not found] <977qHyDIk8016S03.1345865710@web03.cms.usa.net>
2012-08-25 13:58 ` claudio pisani
2012-08-27 22:03 ` David Roberts
2012-08-24 19:03 claudio pisani
2010-02-04 17:39 Question " lamarche
2010-02-06 0:12 ` Toby Bartels
2010-02-06 0:21 ` Steve Lack
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