| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Montpellier, Inst Montpellierain Alexander Grothendieck, CNRS, IMAG, Montpellier - France
[2] Univ Sao Paulo, Dept Matemat, IME, Rua Matao 1010 Cx Pt 20570, Sao Paulo - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 591, p. 117-141, FEB 1 2022. |
| Web of Science Citations: | 0 |
| Abstract | |
Let G be a group acting on a small category Cover 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. (c) 2021 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 14/09310-5 - Algebraic structures and their representations |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Projects - Thematic Grants |