I am learning parts of topos theory and it feels like I am missing something regarding indexed functors.
This comes from the definition of a locally connected geometric morphism $f : E \rightarrow F$ as being essential and the extra adjoint be F-indexed.
I am looking for a definition as I am unfamiliar with indexed category theory. What does it mean for an ordinary functor to be F-indexed, is this some canonical self-indexing of E and F?