Differential torsion theories on Eilenberg-Moore categories of monads
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917760759496704 |
|---|---|
| author | Ahuja, Divya Kour, Surjeet |
| author_facet | Ahuja, Divya Kour, Surjeet |
| contents | Let $\mathcal C$ be a Grothendieck category and $U$ be a monad on $\mathcal C$ that is exact and preserves colimits. In this article, we prove that every hereditary torsion theory on the Eilenberg-Moore category of modules over a monad $U$ is differential. Further, if $δ:U\longrightarrow U$ denotes a derivation on a monad $U$, then we show that every $δ$-derivation on a $U$-module $M$ extends uniquely to a $δ$-derivation on the module of quotients of $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential torsion theories on Eilenberg-Moore categories of monads Ahuja, Divya Kour, Surjeet Category Theory 13N15, 16S90, 18C20, 18E40 Let $\mathcal C$ be a Grothendieck category and $U$ be a monad on $\mathcal C$ that is exact and preserves colimits. In this article, we prove that every hereditary torsion theory on the Eilenberg-Moore category of modules over a monad $U$ is differential. Further, if $δ:U\longrightarrow U$ denotes a derivation on a monad $U$, then we show that every $δ$-derivation on a $U$-module $M$ extends uniquely to a $δ$-derivation on the module of quotients of $M$. |
| title | Differential torsion theories on Eilenberg-Moore categories of monads |
| topic | Category Theory 13N15, 16S90, 18C20, 18E40 |
| url | https://arxiv.org/abs/2407.16782 |