# On homology with coefficients and generalized inductions

## TL;DR

This paper explores how homology of G-posets with G-equivariant coefficients can reconstruct group representation inductions, using local categories of finite groups to unify and extend existing results.

## Contribution

It introduces a framework connecting homology with coefficients to induction processes via local categories, offering new insights and reformulations in group representation theory.

## Key findings

- Homology with G-equivariant coefficients reconstructs induction processes.
- Local categories of finite groups facilitate natural homology constructions.
- Reformulation and extension of existing results in group representations.

## Abstract

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