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• CommentRowNumber1.
• CommentAuthorDavid_Corfield
• CommentTimeAug 25th 2021

Mentioned Pos.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeAug 25th 2021
• (edited Aug 25th 2021)

then best to have a list including also the less exotic examples. Have now started one here.

Also adjusted your line to include pointer to (0,1)-category, in order to bring out the pattern.

And I adjusted the (old) paragraph now right before this list of examples, for generality and hyperlinking.

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeAug 25th 2021

Can we guess what makes a $(1,2)$-topos differ from an ordinary topos from the case of Pos? It contains an object which does what $\bottom \to \top$ does in Pos, i.e., classifying something?

• CommentRowNumber4.
• CommentAuthorMike Shulman
• CommentTimeAug 25th 2021

Classifying sieves = monic fibrations.