Re: V-included categories

[Paul Blain Levy <P.B.Levy@cs.bham.ac.uk>]

On 01/01/18 13:10, Paul Blain Levy 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.
Another advantage: the category of V-included categories is W-small.

Paul

>
> 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
>
>
>



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