Galois measurings for noncommutative base change of entwined contramodule and entwined comodule categories
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915185334157312 |
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| author | Ahuja, Divya Banerjee, Abhishek Kour, Surjeet |
| author_facet | Ahuja, Divya Banerjee, Abhishek Kour, Surjeet |
| contents | We study the noncommutative base change of an entwining structure $(A,C,ψ)$ by a Grothendieck category $\mathfrak S$, using two module like categories. These are the categories of entwined comodule objects and entwined contramodule objects in $\mathfrak S$ over the entwining structure $(A,C,ψ)$. We consider criteria for maps between these noncommutative spaces, induced by generalized maps between entwining structures, known as measurings, to behave like Galois extensions. We also study conditions for extensions of these noncommutative spaces, understood as functors between module like categories, to have separability, Frobenius or Maschke type properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05233 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Galois measurings for noncommutative base change of entwined contramodule and entwined comodule categories Ahuja, Divya Banerjee, Abhishek Kour, Surjeet Rings and Algebras Category Theory 16T15, 18E10, 18E50 We study the noncommutative base change of an entwining structure $(A,C,ψ)$ by a Grothendieck category $\mathfrak S$, using two module like categories. These are the categories of entwined comodule objects and entwined contramodule objects in $\mathfrak S$ over the entwining structure $(A,C,ψ)$. We consider criteria for maps between these noncommutative spaces, induced by generalized maps between entwining structures, known as measurings, to behave like Galois extensions. We also study conditions for extensions of these noncommutative spaces, understood as functors between module like categories, to have separability, Frobenius or Maschke type properties. |
| title | Galois measurings for noncommutative base change of entwined contramodule and entwined comodule categories |
| topic | Rings and Algebras Category Theory 16T15, 18E10, 18E50 |
| url | https://arxiv.org/abs/2503.05233 |