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Resolving by a free action linear category and applications to Hochschild-Mitchell (co)homology.
- Source :
-
Journal of Algebra . Feb2022, Vol. 591, p117-141. 25p. - Publication Year :
- 2022
-
Abstract
- Let G be a group acting on a small category C over a field k , that is C is a G - k -category. We first obtain an unexpected result: C is resolvable by a category which is G - k -equivalent to it, on which G acts freely on objects. This resolving 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 C are isomorphic to the trivial component of the Hochschild-Mitchell (co)homology of the skew category C [ G ]. If the action of G is free on objects, then there is a canonical decomposition of the Hochschild-Mitchell (co)homology of the quotient category 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 591
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 153658396
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2021.10.020