From: Michael Shulman <shulman@sandiego.edu>
To: Paul Blain Levy <P.B.Levy@cs.bham.ac.uk>
Cc: "Categories list <Categories list>" <categories@mta.ca>
Subject: Re: V-included categories
Date: Tue, 2 Jan 2018 11:15:34 -0800 [thread overview]
Message-ID: <E1eWklO-0004n3-7T@mlist.mta.ca> (raw)
In-Reply-To: <E1eW4Dd-0003rd-K8@mlist.mta.ca>
I believe that in his paper "Notions of topos" Ross Street used the
name "V-moderate category" for this or a closely related notion.
There the point was that V-moderate categories have another advantage
over locally V-small ones, namely that their objects can (assuming the
axiom of choice) be well-ordered with all initial segments being
V-small.
On Mon, Jan 1, 2018 at 5:10 AM, Paul Blain Levy <P.B.Levy@cs.bham.ac.uk> wrote:
>
> 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:[~2018-01-02 19:15 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
[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 [this message]
[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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