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In group representations several inductions given by tensoring withappropriate bimodules may be reconstructed via homology of $G$-posets with$G$-equivariant coefficients. For this purpose, we need various localcategories of a finite group $G$, which afford the coefficients. Consequently,the functors among local categories give rise to the homology constructionsnaturally, and may be used to reformulate some existing results, as well as todeduce new statements.

On homology with coefficients and generalized inductions