Re: Hecke eigensheaves and KV 2-vectors

I wrote:

You're asking about something more general: "weak eigenobjects" of endofunctors T: C -> C on *monoidal* categories C. In other words: objects c in C equipped with isomorphisms Tc -> a tensor c for some fixed object a.

Sorry! Actually Urs is asking about an even more general situation. A is a monoidal category, C is a category tensored over A, T: C -> C, and we seek objects c in C equipped with isomorphisms Tc -> a tensor c for some fixed object a. We can form the category of these, which is the pseudo-equalizer of T and a tensor -, and call it an "eigenspace of T". For Urs, A = Vect and C is a Vect-module. Best, jb