Hochschild cohomology in toposes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914711602200576 |
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| author | Michie, Cameron Tomasic, Ivan |
| author_facet | Michie, Cameron Tomasic, Ivan |
| contents | We develop a theory of internal Hochschild cohomology in a ringed topos. We construct it via the internal Hochschild cochain complex, as well as through derived functor/topos cohomology theory, and discuss its relationship to the absolute Hochschild cohomology.
By specialising to the topos of difference sets, we obtain a theory of internal difference Hochschild cohomology, and compare it to the absolute Hochschild cohomology through the Grothendieck and hypercohomology spectral sequences.
We provide a systematic and detailed treatment of tensor products in suitable toposes in hope to complete the existing literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hochschild cohomology in toposes Michie, Cameron Tomasic, Ivan Category Theory Logic Rings and Algebras 18B25, 13D03 We develop a theory of internal Hochschild cohomology in a ringed topos. We construct it via the internal Hochschild cochain complex, as well as through derived functor/topos cohomology theory, and discuss its relationship to the absolute Hochschild cohomology. By specialising to the topos of difference sets, we obtain a theory of internal difference Hochschild cohomology, and compare it to the absolute Hochschild cohomology through the Grothendieck and hypercohomology spectral sequences. We provide a systematic and detailed treatment of tensor products in suitable toposes in hope to complete the existing literature. |
| title | Hochschild cohomology in toposes |
| topic | Category Theory Logic Rings and Algebras 18B25, 13D03 |
| url | https://arxiv.org/abs/2403.08087 |