Lax structures in 2-category theory
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908304296378368 |
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| author | Štěpán, Miloslav |
| author_facet | Štěpán, Miloslav |
| contents | This thesis focuses on topics in 2-category theory: in particular on double categories, pseudomonads and codescent objects. In Chapter 2 we recall all the necessary notions. In Chapter 3 we show that factorization systems can be equivalently described as double categories satisfying certain properties. In Chapter 4 we focus on turning weak (colax) structures into strict ones in a universal way - this covers for instance colax monoidal categories or lax functors. In Chapter 5 we study the Kleisli 2-category for a lax-idempotent pseudomonad, the application of which is establishing weak cocompleteness of 2-categories such as the one of monoidal categories and lax monoidal functors. Finally, Chapter 6 focuses on the process of turning any 2-monad into a lax-idempotent one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04467 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lax structures in 2-category theory Štěpán, Miloslav Category Theory 18N10, 18N15, 18D60, 18D65, 18C20, 18A32, 18B10, 18M05 This thesis focuses on topics in 2-category theory: in particular on double categories, pseudomonads and codescent objects. In Chapter 2 we recall all the necessary notions. In Chapter 3 we show that factorization systems can be equivalently described as double categories satisfying certain properties. In Chapter 4 we focus on turning weak (colax) structures into strict ones in a universal way - this covers for instance colax monoidal categories or lax functors. In Chapter 5 we study the Kleisli 2-category for a lax-idempotent pseudomonad, the application of which is establishing weak cocompleteness of 2-categories such as the one of monoidal categories and lax monoidal functors. Finally, Chapter 6 focuses on the process of turning any 2-monad into a lax-idempotent one. |
| title | Lax structures in 2-category theory |
| topic | Category Theory 18N10, 18N15, 18D60, 18D65, 18C20, 18A32, 18B10, 18M05 |
| url | https://arxiv.org/abs/2504.04467 |