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Autre Publication Scientifique Journal of Algebra Année : 2023

Strongly stratifying ideals, Morita contexts and Hochschild homology

Marcelo Lanzilotta
  • Fonction : Auteur
Eduardo Marcos
Andrea Solotar
  • Fonction : Auteur

Résumé

Let $G$ be a group acting on a small category $\mathcal C$ over a field $k$, that is $\mathcal C$ is a $G$-$k$-category. We first obtain that $\mathcal C$ is resolvable by a category which is $G$-$k$-equivalent to it, on which $G$ acts freely on objects. This resolvent category enables to show that if the coinvariants and the invariants functors are exact, then the coinvariants and invariants of the Hochschild-Mitchell (co)homology of $\mathcal C$ are isomorphic to the trivial component of the Hochschild-Mitchell (co)ho\-mo\-logy of the skew category $\mathcal C[G]$. Otherwise the corresponding spectral sequence can be settled. If the action of $G$ is free on objects, there is a canonical decomposition of the Hochschild-Mitchell (co)homology of the quotient category $\mathcal C/G$ along the conjugacy classes of $G$. This way we provide a general frame for monomorphisms which have been described previously in low degrees.

Dates et versions

hal-04252063 , version 1 (31-03-2023)
hal-04252063 , version 2 (20-10-2023)

Identifiants

Citer

Claude Cibils, Marcelo Lanzilotta, Eduardo Marcos, Andrea Solotar. Strongly stratifying ideals, Morita contexts and Hochschild homology. 2023, pp.117-141. ⟨10.1016/j.jalgebra.2023.09.044⟩. ⟨hal-04252063v2⟩
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