LHS-spectral sequences for regular extensions of categories
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909088787464192 |
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| author | Yalcin, Ergun |
| author_facet | Yalcin, Ergun |
| contents | In [F. Xu, On the cohomology rings of small categories, J. Pure Appl. Algebra 212 (2008), 2555-2569], Xu constructs a LHS-spectral sequence for target regular extensions of small categories. We extend this construction to ext-groups and construct a similar spectral sequence for source regular extensions (with right module coefficients). As a special case of these LHS-spectral sequences, we obtain three different versions of Slominska's spectral sequence for the cohomology of regular EI-categories. We show that many well-known spectral sequences related to the homology decompositions of finite groups, centric linking systems, and the orbit category of fusion systems can be obtained as the LHS-spectral sequence of an extension. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_02000 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | LHS-spectral sequences for regular extensions of categories Yalcin, Ergun Algebraic Topology Primary: 18G40, Secondary: 55R35, 18G15, 20J06, 55N91 In [F. Xu, On the cohomology rings of small categories, J. Pure Appl. Algebra 212 (2008), 2555-2569], Xu constructs a LHS-spectral sequence for target regular extensions of small categories. We extend this construction to ext-groups and construct a similar spectral sequence for source regular extensions (with right module coefficients). As a special case of these LHS-spectral sequences, we obtain three different versions of Slominska's spectral sequence for the cohomology of regular EI-categories. We show that many well-known spectral sequences related to the homology decompositions of finite groups, centric linking systems, and the orbit category of fusion systems can be obtained as the LHS-spectral sequence of an extension. |
| title | LHS-spectral sequences for regular extensions of categories |
| topic | Algebraic Topology Primary: 18G40, Secondary: 55R35, 18G15, 20J06, 55N91 |
| url | https://arxiv.org/abs/2305.02000 |