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New entry representable morphism, in the sense of Grothendieck school. The notion is used at closed immersion of schemes where I just made some changes.
I have added a link to the existing representable morphism of stacks
Oh thanks, I forgot of its existence. It will need more work though… :=)
I clarified representable morphism as suggested by a query, and removed the query.
Are there any category theoretic references on this notion? Everything I’ve found has been geometry related.
Well, there’s Natural models of type theory…
Yes thats what I’ve been reading, I haven’t made this clear. It seems strange to me no category theorists have studied this notion since Grothendieck. In fact Awodey is the only writing I could find that uses it for reasons other than geometry.
By the way, regarding #7, I believe representable morphisms (of $Cat$-valued (pre)sheaves, rather than sheaves of sets) are implicitly present in the discussion of “comprehension schemes” in section B1.3 of Sketches of an Elephant. But it’s some work to extract them.
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