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Stream: deprecated: topos theory

Topic: Logical structure associated to toposes

Kobe Wullaert (Jul 20 2023 at 11:51):

Hi everyone
Every (elementary) topos induces some logical structure, e.g.,:

• a (first-order) hyperdoctrine; by mapping an object to the Heyting algebra of its subobjects;
• a model of type theory, such as a category with attributes (or a comprehension structure); because a topos is locally cartesian closed.

My question is whether this connection has been studied in more detail, e.g., whether it possible to recognize (characterize) which hyperdoctrines/comprehension categories arise from a (elementary) topos?

Morgan Rogers (he/him) (Jul 20 2023 at 12:25):

@Davide Trotta could likely answer that question, although he is infrequently active here. Try sending him an email.

Kobe Wullaert (Jul 20 2023 at 12:35):

Morgan Rogers (he/him) said:

Davide Trotta could likely answer that question, although he is infrequently active here. Try sending him an email.

Thank you!

James Deikun (Jul 21 2023 at 12:07):

Bart Jacobs's Categorical Logic has some characterizations along these lines, although maybe not the exact ones you're looking for.