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Adjunctions induced by Kan Extensions between Grothendieck Toposes

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If you have a question about this talk, please contact Sean Moss .

It is well know that a flat functor between two small categories will induce an adjoint triple between the respective presheaf categories via left and right Kan extensions. I will explain how certain conditions imposed on the flat functor can enable us to restrict this adjunction to subcategories of sheaves, and I will comment on the significance of this in the study of local geometric morphisms.

I will briefly sketch a gentle introduction to Kan extensions for those who aren’t yet familiar with them.

This talk is part of the Junior Category Theory Seminar series.

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