The least subtopos containing the discrete skeleton of $Ω$
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914895942909952 |
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| author | Menni, Matí as |
| author_facet | Menni, Matí as |
| contents | Let $p: \mathcal{E} \to \mathcal{S}$ be a pre-cohesive geometric morphism. We show that the least subtopos of $\mathcal{E}$ containing both the subcategories $p^*: \mathcal{S} \to \mathcal{E}$ and $p^!: \mathcal{S} \to \mathcal{E}$ exists, and that it coincides with the least subtopos containing $p^*2$, where 2 denotes the subobject classifier of $\mathcal{S}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The least subtopos containing the discrete skeleton of $Ω$ Menni, Matí as Category Theory 18B25, 18F10 Let $p: \mathcal{E} \to \mathcal{S}$ be a pre-cohesive geometric morphism. We show that the least subtopos of $\mathcal{E}$ containing both the subcategories $p^*: \mathcal{S} \to \mathcal{E}$ and $p^!: \mathcal{S} \to \mathcal{E}$ exists, and that it coincides with the least subtopos containing $p^*2$, where 2 denotes the subobject classifier of $\mathcal{S}$. |
| title | The least subtopos containing the discrete skeleton of $Ω$ |
| topic | Category Theory 18B25, 18F10 |
| url | https://arxiv.org/abs/2408.00514 |