Characterizations of higher derivations and higher differential torsion theories in Eilenberg-Moore categories of monads
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908790945742848 |
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| author | Paik, Dipti Ahuja, Divya Kour, Surjeet |
| author_facet | Paik, Dipti Ahuja, Divya Kour, Surjeet |
| contents | Let $T$ be a monad on a category $\mathscr{C}$. In this paper, we introduce the notion of higher derivations on the monad $T$ and characterize them in terms of ordinary derivations on $T$. We also define higher derivations on modules over the monad $T$ in the Eilenberg-Moore category $EM_T$ and establish their characterization in a similar manner. We provide several examples that illustrate and support our results. Furthermore, we examine the conditions under which a torsion theory on $EM_T$ is higher differential, and show that this holds if and only if every higher derivation on a module $M \in EM_T$ extends uniquely to its module of quotients $Q_τ(M)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19200 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterizations of higher derivations and higher differential torsion theories in Eilenberg-Moore categories of monads Paik, Dipti Ahuja, Divya Kour, Surjeet Category Theory (2020):13N15, 16S90, 18C20, 18E40 Let $T$ be a monad on a category $\mathscr{C}$. In this paper, we introduce the notion of higher derivations on the monad $T$ and characterize them in terms of ordinary derivations on $T$. We also define higher derivations on modules over the monad $T$ in the Eilenberg-Moore category $EM_T$ and establish their characterization in a similar manner. We provide several examples that illustrate and support our results. Furthermore, we examine the conditions under which a torsion theory on $EM_T$ is higher differential, and show that this holds if and only if every higher derivation on a module $M \in EM_T$ extends uniquely to its module of quotients $Q_τ(M)$. |
| title | Characterizations of higher derivations and higher differential torsion theories in Eilenberg-Moore categories of monads |
| topic | Category Theory (2020):13N15, 16S90, 18C20, 18E40 |
| url | https://arxiv.org/abs/2601.19200 |