Double factorization systems in equivariant topology and topos theory
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913999074885632 |
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| author | Martyanov, E. V. |
| author_facet | Martyanov, E. V. |
| contents | In the present work, we investigate the extension of double factorization systems to the categories of Eilenberg-Moore (co)algebras. We show that the double factorization systems $(\texttt{ExEpi},\texttt{Bim},\texttt{ExMono})$ in the categories $\mathbf{Tych}$, $\mathbf{Unif}$ and $\mathbf{Comp}$ extend to the same double factorization systems in the corresponding categories of Eilenberg-Moore algebras $\mathbf{Tych}^{\mathbb{H}^t}$, $\mathbf{Unif}^{\mathbb{H}^u}$ and $\mathbf{Comp}^{\mathbb{H}^c}$. We establish a connection between cartesian double factorization systems and LT-topologies. We provide sufficient conditions for the extension of cartesian double factorization systems to the topos of coalgebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_14981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Double factorization systems in equivariant topology and topos theory Martyanov, E. V. General Topology 54E15, 54H15, 54B30 (Primary) 18A32, 18B25, 18C15 (Secondary) In the present work, we investigate the extension of double factorization systems to the categories of Eilenberg-Moore (co)algebras. We show that the double factorization systems $(\texttt{ExEpi},\texttt{Bim},\texttt{ExMono})$ in the categories $\mathbf{Tych}$, $\mathbf{Unif}$ and $\mathbf{Comp}$ extend to the same double factorization systems in the corresponding categories of Eilenberg-Moore algebras $\mathbf{Tych}^{\mathbb{H}^t}$, $\mathbf{Unif}^{\mathbb{H}^u}$ and $\mathbf{Comp}^{\mathbb{H}^c}$. We establish a connection between cartesian double factorization systems and LT-topologies. We provide sufficient conditions for the extension of cartesian double factorization systems to the topos of coalgebras. |
| title | Double factorization systems in equivariant topology and topos theory |
| topic | General Topology 54E15, 54H15, 54B30 (Primary) 18A32, 18B25, 18C15 (Secondary) |
| url | https://arxiv.org/abs/2508.14981 |