* Re: Sheaf terminology question
@ 2018-07-17 8:48 Zoran Škoda
0 siblings, 0 replies; 3+ messages in thread
From: Zoran Škoda @ 2018-07-17 8:48 UTC (permalink / raw)
To: Andrew Pitts; +Cc: Categories
Late Alexander L. Rosenberg used the term epipresheaf in that case; I am
not sure if he learned it somewhere or he made it up. The reasoning behind
the terminology is clear.
Zoran Škoda
On 16 Jul 2018 14:10, "Andrew Pitts" <andrew.pitts@cl.cam.ac.uk> wrote:
> Given a coverage on a small category, the condition for a Set-valued
> presheaf on the category to be a sheaf has an existence part and a
> uniqueness part. If only the uniqueness part holds, one says that the
> presheaf is separated. Is there a name out there for presheaves that only
> satisfy the existence part of the sheaf condition?
>
> Andy Pitts
>
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
^ permalink raw reply [flat|nested] 3+ messages in thread
* Re: Sheaf terminology question
2018-07-13 14:10 Andrew Pitts
@ 2018-07-18 8:56 ` Andrew Pitts
0 siblings, 0 replies; 3+ messages in thread
From: Andrew Pitts @ 2018-07-18 8:56 UTC (permalink / raw)
To: categories
> On 13 Jul 2018, at 15:10, Andrew Pitts <Andrew.Pitts@cl.cam.ac.uk> wrote:
>
> Given a coverage on a small category, the condition for a Set-valued presheaf on the category to be a sheaf has an existence part and a uniqueness part. If only the uniqueness part holds, one says that the presheaf is separated. Is there a name out there for presheaves that only satisfy the existence part of the sheaf condition?
Many thanks to those who responded with suggestions. I won’t repeat replies that were also sent to categories@mta.ca, but there were a couple sent privately that I pass on:
Peter Johnstone reminded me of the fact that category-theorists tend to use the prefix “weak” to remove the uniqueness part of a unique existence condition. So one could speak of "weak sheaves". (A slight problem with that is that when I say it, it sounds a lot like wheat sheaves :-).)
Tom Hirschowitz pointed out that there is the concept of effective descent data in stack theory, so one might use the term “effective presheaf” for what I was referring to. I quite like that.
Andy
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
^ permalink raw reply [flat|nested] 3+ messages in thread
* Sheaf terminology question
@ 2018-07-13 14:10 Andrew Pitts
2018-07-18 8:56 ` Andrew Pitts
0 siblings, 1 reply; 3+ messages in thread
From: Andrew Pitts @ 2018-07-13 14:10 UTC (permalink / raw)
To: categories
Given a coverage on a small category, the condition for a Set-valued presheaf on the category to be a sheaf has an existence part and a uniqueness part. If only the uniqueness part holds, one says that the presheaf is separated. Is there a name out there for presheaves that only satisfy the existence part of the sheaf condition?
Andy Pitts
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
^ permalink raw reply [flat|nested] 3+ messages in thread
end of thread, other threads:[~2018-07-18 8:56 UTC | newest]
Thread overview: 3+ messages (download: mbox.gz / follow: Atom feed)
-- links below jump to the message on this page --
2018-07-17 8:48 Sheaf terminology question Zoran Škoda
-- strict thread matches above, loose matches on Subject: below --
2018-07-13 14:10 Andrew Pitts
2018-07-18 8:56 ` Andrew Pitts
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).