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In the spirit of Ronnie brown's answer to this post, I was wondering whether there are any connections between topos theory and geometric group theory.

The question might seem strange, but it is motivated by some references about Sheaves on Graphs I have been told about. Since I know very few things about this, I was trying to understand whether there are connections with fields, as geometric group theory, which are more familiar to me.

Thank you in advance for any suggestion; I hope that you will forgive me for the somehow strange kind of the question.

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As far as I can tell, topoi have no connection to mathematics outside of algebraic geometry and logic. In contrast, sheaves (on topological spaces) are a standard tool in complex analysis, general and algebraic topology (as well as algebraic geometry, of course). I know only of one application of sheaves on graphs to geometric group theory.

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  • $\begingroup$ An example of applications of toposes in applied mathematics that I particularly like is temporal type theory. If I remember Spivak's talk at the Como topos event correctly, they applied this in the real world, that is, at a company. $\endgroup$ – Ingo Blechschmidt Dec 16 '18 at 22:37

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