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Stream: deprecated: topos theory

Topic: essential geometric morphism

vikraman (Mar 27 2020 at 18:45):

A functor $F : C \rightarrow D$ gives an essential geometric morphism between toposes $\hat{C}$ and $\hat{D}$, these are given by pre-composition, left, and right kan extensions. We have the same situation for V-enriched categories $C$ and $D$ and their V-enriched presheaf categories, taking V to be a cosmos. Is there a name for this construction, or is it written down somewhere?

Morgan Rogers (he/him) (Mar 27 2020 at 18:56):

Beyond "essential geometric morphism induced by $F$", I'm not personally aware of any particular name. :thinking:
Or perhaps not everyone calls them geometric morphisms in the enriched setting?