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Morgan Rogers (he/him) (Jul 23 2020 at 12:12):Sebastiano Vigna's A Guided Tour in the Topos of Graphs is a nice read, but topos theory is too vast to study it all in this context in a single paper. I wonder if anyone has considered this topos as a classifying topos? I have a nice description of the theory classified by this topos in mind, which I could express as a sketch, but I'm curious if anyone has put any effort into expressing/interpreting a theory classified by this topos before me.
Morgan Rogers (he/him) (Jul 23 2020 at 12:15):Perhaps Lawvere? Although one must be careful to distinguish between the reflexive and non-reflexive cases.