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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.00380 |
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| _version_ | 1866917013773877248 |
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| author | Di Liberti, Ivan Lobbia, Gabriele Sousa, Lurdes |
| author_facet | Di Liberti, Ivan Lobbia, Gabriele Sousa, Lurdes |
| contents | We introduce the notion of Kan injectivity in 2-categories and study its properties. For an adequate 2-category $\mathcal{K}$, we show that every set of morphisms $\mathcal{H}$ induces a KZ-pseudomonad on $\mathcal{K}$ whose 2-category of pseudoalgebras is the locally full sub-2-category of all objects (left) Kan injective with respect to $\mathcal{H}$ and morphisms preserving Kan extensions. The main ingredient is the construction of a (pseudo)chain whose appropriate ``convergence" is ensured by a small object argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00380 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | KZ-pseudomonads and Kan Injectivity Di Liberti, Ivan Lobbia, Gabriele Sousa, Lurdes Category Theory 18D70, 18D65, 18N10, 18N15 We introduce the notion of Kan injectivity in 2-categories and study its properties. For an adequate 2-category $\mathcal{K}$, we show that every set of morphisms $\mathcal{H}$ induces a KZ-pseudomonad on $\mathcal{K}$ whose 2-category of pseudoalgebras is the locally full sub-2-category of all objects (left) Kan injective with respect to $\mathcal{H}$ and morphisms preserving Kan extensions. The main ingredient is the construction of a (pseudo)chain whose appropriate ``convergence" is ensured by a small object argument. |
| title | KZ-pseudomonads and Kan Injectivity |
| topic | Category Theory 18D70, 18D65, 18N10, 18N15 |
| url | https://arxiv.org/abs/2211.00380 |