Functorial languages in homological algebra and lower central series
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911053174013952 |
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| author | Golub, Nikita Ionin, Vasily Mukoseev, Lev |
| author_facet | Golub, Nikita Ionin, Vasily Mukoseev, Lev |
| contents | There is a general phenomenon in algebra that numerous functors of homological significance admit characterization as derived limits of elementary functors defined over categories of free extensions. We demonstrate that upon restriction to appropriate subcategories of the category of groups, one may express analogously more interesting functors, including homology groups with cyclic coefficients.
Moreover, we are laying the foundations of the so-called $\mathbf{fr}_\infty$-language, extending the $\mathbf{fr}$-language of Roman Mikhailov and Sergei O. Ivanov. This language is constructed by augmenting the $\mathbf{fr}$-language through the introduction of an infinite family of letters $\mathbf{fr}$ corresponding to the lower central series $γ_m(R)$ of the group of relations and leads to some neat computations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_05708 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functorial languages in homological algebra and lower central series Golub, Nikita Ionin, Vasily Mukoseev, Lev K-Theory and Homology Group Theory There is a general phenomenon in algebra that numerous functors of homological significance admit characterization as derived limits of elementary functors defined over categories of free extensions. We demonstrate that upon restriction to appropriate subcategories of the category of groups, one may express analogously more interesting functors, including homology groups with cyclic coefficients. Moreover, we are laying the foundations of the so-called $\mathbf{fr}_\infty$-language, extending the $\mathbf{fr}$-language of Roman Mikhailov and Sergei O. Ivanov. This language is constructed by augmenting the $\mathbf{fr}$-language through the introduction of an infinite family of letters $\mathbf{fr}$ corresponding to the lower central series $γ_m(R)$ of the group of relations and leads to some neat computations. |
| title | Functorial languages in homological algebra and lower central series |
| topic | K-Theory and Homology Group Theory |
| url | https://arxiv.org/abs/2410.05708 |