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At Frobenius reciprocity I can see Frobenius reciprocity can be formulated in very general terms and that the classical adjoint pair in the theory of finite dimensional representations of finite groups $Hom_H(W,Res(V))=Hom_G(Ind(W),V)$ with $H$ a subgroup of $G$ is just a very particular case of the general theory. However, this familiar case has (to me) the advantage that I know how to explicitly compute $Ind(W)$ for a given representation $W$ of $H$ and how to prove the adjointness between $Res$ and $Ind$ by hand. So I’m wondering about what can be said about linear 2-representations of finite groups (with, I guess, some finiteness assumptions I’m not able to specify at the moment). For instance, if we take as a model for $2Vect$ the 2-category algebras/bimodules/bimodule morphisms then I have a clear idea of what the explcit data of a representation of a finite group $G$ with values in $2Vect$ are, and can easily write a restriction functor $Res$ from 2-representations of $G$ with values in $2Vect$ to 2-representations of a subgroup $H$ with values in $2Vect$. Does ths have an adjoint $Ind$? How is this explicitely described? (I should be able to work this out by myself by thinking to it enough, but I would like not to loose time on this if it is already well known and a pointer to the literature will solve this)
the not-the-same-but-related “KV” model of 2Vect
It’s a sub-model. KV 2-vector spaces form a sub-2-category of those that Domenico mentioned.
Hi Bruce,
Thanks a lot!
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