From: Eduardo Julio Dubuc <edubuc@dm.uba.ar>
To: Paul Blain Levy <P.B.Levy@cs.bham.ac.uk>,
"Categories list\" <Categories list>" <categories@mta.ca>
Subject: Re: V-included categories
Date: Mon, 1 Jan 2018 18:14:20 -0300 [thread overview]
Message-ID: <E1eWMfC-00084s-6W@mlist.mta.ca> (raw)
In-Reply-To: <E1eW4Dd-0003rd-K8@mlist.mta.ca>
Have you considered the following at the very begining of SGA4:
Remarque 1.1.2. ??? Soit D une cat??gorie poss??dant les propri??t??s suivantes :
(C1) L???ensemble ob(D) est contenu dans l???univers U .
(C2) Pour tout couple (x, y) d???objets de D, l???ensemble HomD(x, y) est un
??l??ment de U .
(Les cat??gories usuelles construites ?? partir d???un univers U poss??dent
ces deux propri??t??s: U -Ens, U -Ab,. . .).
Soit C une cat??gorie appartenant ?? U . Alors la cat??gorie
Fonct(C, D) ne poss??de pas en g??n??ral les propri??t??s (C1) et (C2). Par
exemple la cat??gorie Fonct(C,U-Ens) ne poss??de aucune des propri??t??s
(C1) et (C2).
C???est ce qui justifie la d??finition adopt??e de U-cat??gorie, de
pr??f??rence ?? la notion plus restrictive par les conditions (C1) et (C2)
ci-dessus.
best e.d.
El 1/1/18 a las 10:10, Paul Blain Levy escribi??:
>
> Hi,
>
> Let V be a Grothendieck universe.?? A "V-set" is an element of V, and a
> "V-class" is a subset of V.
>
> Say that a category C is "V-included" when it has the following two
> properties.
>
> (1) ob C is a V-class.
>
> (2) C(x,y) is a V-set for all x,y in ob C.
>
> The advantage of V-inclusion over local V-smallness (i.e. condition (2)
> alone) is that V-included categories are W-small for every universe W
> greater than V, whereas locally V-small categories are not, in general.
>
> Furthermore, all the standard categories constructed from V are
> V-included.?? (Except for the ones that are not even locally V-small,
> like the category of V-included categories.)
>
> Is there a standard name for V-inclusion?
>
> Paul
>
>
>
>
>
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next prev parent reply other threads:[~2018-01-01 21:14 UTC|newest]
Thread overview: 11+ messages / expand[flat|nested] mbox.gz Atom feed top
2018-01-01 13:10 Paul Blain Levy
2018-01-01 18:28 ` Paul Blain Levy
2018-01-01 21:14 ` Eduardo Julio Dubuc [this message]
[not found] ` <e962e844-fa2d-5a56-e3e7-be308a483c12@dm.uba.ar>
2018-01-01 22:46 ` Paul Blain Levy
2018-01-02 18:40 ` rosicky
2018-01-02 19:15 ` Michael Shulman
[not found] ` <03876a66-f7ee-a161-091c-32944a0d8556@dm.uba.ar>
2018-01-03 6:44 ` Paul Blain Levy
[not found] ` <E1eWtjA-0006aj-48@mlist.mta.ca>
[not found] ` <918B0A9E-DFD0-4033-AB7A-1A8A364DB8A9@cs.bham.ac.uk>
[not found] ` <20180104110046.GA24344@mathematik.tu-darmstadt.de>
2018-01-04 20:47 ` Steve Vickers
[not found] ` <5c1ec079-335b-5609-9cb7-ae4e519f6716@dm.uba.ar>
2018-01-04 21:20 ` Thomas Streicher
[not found] ` <C16D1DBE-89F3-42EC-86A0-B69B5DBF5713@cs.bham.ac.uk>
2018-01-04 21:30 ` Thomas Streicher
[not found] ` <E1eWtkf-0006d1-O1@mlist.mta.ca>
2018-01-04 23:28 ` Richard Williamson
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