Homology of sheaves via Brown representability

TL;DR

This paper presents an elementary construction of sheaf homology using Brown representability, simplifying the derivation of its properties and connecting it with duality theories and group homology.

Contribution

It introduces a new, simplified approach to sheaf homology based on Brown representability, linking it to duality and group homology.

Findings

Homology of sheaves constructed via Brown representability.

Main properties derived straightforwardly from the construction.

Connections established with Poincaré-Verdier duality and group homology.

Abstract

We give an elementary construction of homology of sheaves from Brown representability for the dual and see how its main properties are derived easily from the construction. Comparison with Poincar\'e-Verdier duality and with homology of groups are also developed.