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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 3rd 2010

expanded concrete sheaf: added the precise definition and some important properties.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJan 26th 2011

I have added to concrete sheaf a subsection Slice topos over a concrete object with some observations.

Not sure how useful this is.

• CommentRowNumber3.
• CommentAuthorSam Staton
• CommentTimeAug 5th 2019

mention well-pointedness and concrete categories. Hope I got this right.

• CommentRowNumber4.
• CommentAuthorMike Shulman
• CommentTimeAug 5th 2019

Removed the link to well-pointedness; I think the latter term is usually only used for toposes.

• CommentRowNumber5.
• CommentAuthorSam Staton
• CommentTimeAug 6th 2019

Hi, Actually the term is quite widely used for ccc’s, at least in CS, e.g. in

• CommentRowNumber6.
• CommentAuthorMike Shulman
• CommentTimeAug 6th 2019

Okay; but in that case the link shouldn’t go to well-pointed topos.

• CommentRowNumber7.
• CommentAuthorSam Staton
• CommentTimeAug 8th 2019
• (edited Aug 8th 2019)
I see. But the well-pointed topos page already mentions some generalizations (pretoposes, coherent categories). I thought there might be an external/internal theorem for concrete quasitoposes generalizing the theorem for well-pointed toposes. Although I can't find a reference so maybe there isn't in general?
• CommentRowNumber8.
• CommentAuthorMike Shulman
• CommentTimeAug 8th 2019

True, but an arbitrary ccc seems to me like a much further step than a pretopos. And the page points out that the “correct” definition differs depending on what kind of category we’re talking about. In particular, it suggests that for a finite-limit category we should ask that $1$ be a strong generator, not just a generator as it is for a concrete category.

I haven’t thought about well-pointed quasitoposes at all.