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arxiv: 1904.01877 · v2 · pith:ADNIFP6Enew · submitted 2019-04-03 · 🧮 math.AG · math.AT· math.CT

On coherent topoi & coherent 1-localic infty-topoi

classification 🧮 math.AG math.ATmath.CT
keywords coherentinftytopoicategorylocalicsensealgebraiccollect
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In this note we prove the following useful fact that seems to be missing from the literature: the $\infty$-category of coherent ordinary topoi (in the sense of SGA4) is equivalent to the $\infty$-category of coherent $1$-localic $\infty$-topoi (in Lurie's sense). We also collect a number of examples of coherent geometric morphisms between $\infty$-topoi coming from algebraic geometry.

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