On the FI-homology of the injective cogenerators

Geoffrey Powell (1)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

The purpose of this paper is to give information on the FI-homology of the standard injective cogenerators of the category of FI-modules, where FI is the category of finite sets and injections. Working over a field k of characteristic zero, a full calculation is given in homological degree zero and a conjectural description in higher homological degree. The proof of the main theorem reduces to a calculation in representation theory of the symmetric groups, exploiting the Young orthonormal basis.

Domaines: Topologie algébrique [math.AT]

Geoffrey Powell. On the FI-homology of the injective cogenerators. 2022. ⟨hal-03781140⟩