Completeness of quantaloid-enriched categories up to Morita equivalence
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918212707287040 |
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| author | Tang, Xiaoye |
| author_facet | Tang, Xiaoye |
| contents | For a small quantaloid $\mathcal{Q}$, we introduce $\mathcal{M}$-(co)complete $\mathcal{Q}$-categories, i.e., (co)complete $\mathcal{Q}$-categories up to Morita equivalence, as Eilenberg--Moore algebras of the presheaf monad on the category of $\mathcal{Q}$-categories and left adjoint $\mathcal{Q}$-distributors, and characterize such $\mathcal{Q}$-categories through $\mathcal{M}$-(co)tensoredness and $\mathcal{M}$-conical (co)completeness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Completeness of quantaloid-enriched categories up to Morita equivalence Tang, Xiaoye Category Theory For a small quantaloid $\mathcal{Q}$, we introduce $\mathcal{M}$-(co)complete $\mathcal{Q}$-categories, i.e., (co)complete $\mathcal{Q}$-categories up to Morita equivalence, as Eilenberg--Moore algebras of the presheaf monad on the category of $\mathcal{Q}$-categories and left adjoint $\mathcal{Q}$-distributors, and characterize such $\mathcal{Q}$-categories through $\mathcal{M}$-(co)tensoredness and $\mathcal{M}$-conical (co)completeness. |
| title | Completeness of quantaloid-enriched categories up to Morita equivalence |
| topic | Category Theory |
| url | https://arxiv.org/abs/2511.17024 |