Simplicial approach to path homology of quivers, marked categories, groups and algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913237731115008 |
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| author | Ivanov, Sergei O. Pavutnitskiy, Fedor |
| author_facet | Ivanov, Sergei O. Pavutnitskiy, Fedor |
| contents | We develop a generalisation of the path homology theory introduced by Grigor'yan, Lin, Muranov and Yau (GLMY-theory) in a general simplicial setting. The new theory includes as particular cases the GLMY-theory for path complexes and new homology theories: path homology of categories with a chosen set of morphisms (marked categories) groups with a chosen subset (marked groups) and path Hochschild homology of algebras with chosen vector subspaces (marked algebras). Using our general machinery, we also introduce a new homology theory for quivers that we call square-commutative homology of quivers and compare it with the theory developed by Grigor'yan, Muranov, Vershinin and Yau. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06202 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Simplicial approach to path homology of quivers, marked categories, groups and algebras Ivanov, Sergei O. Pavutnitskiy, Fedor Algebraic Topology K-Theory and Homology We develop a generalisation of the path homology theory introduced by Grigor'yan, Lin, Muranov and Yau (GLMY-theory) in a general simplicial setting. The new theory includes as particular cases the GLMY-theory for path complexes and new homology theories: path homology of categories with a chosen set of morphisms (marked categories) groups with a chosen subset (marked groups) and path Hochschild homology of algebras with chosen vector subspaces (marked algebras). Using our general machinery, we also introduce a new homology theory for quivers that we call square-commutative homology of quivers and compare it with the theory developed by Grigor'yan, Muranov, Vershinin and Yau. |
| title | Simplicial approach to path homology of quivers, marked categories, groups and algebras |
| topic | Algebraic Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2211.06202 |