Ultracategories as colax algebras for a pseudo-monad on CAT
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911118192017408 |
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| author | Hamad, Ali |
| author_facet | Hamad, Ali |
| contents | We show a result inspired by a conjecture by Shulman claiming that ultracategories as defined by Lurie are normal colax algebras for a certain pseudo-monad on the category of categories CAT. Such definition allows us to regard left and right ultrafunctors as defined by Lurie as instances of lax/colax algebras morphisms |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20597 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ultracategories as colax algebras for a pseudo-monad on CAT Hamad, Ali Category Theory 18C15, 18N15, 18N10, 03C20 We show a result inspired by a conjecture by Shulman claiming that ultracategories as defined by Lurie are normal colax algebras for a certain pseudo-monad on the category of categories CAT. Such definition allows us to regard left and right ultrafunctors as defined by Lurie as instances of lax/colax algebras morphisms |
| title | Ultracategories as colax algebras for a pseudo-monad on CAT |
| topic | Category Theory 18C15, 18N15, 18N10, 03C20 |
| url | https://arxiv.org/abs/2502.20597 |