Invertible cells in $ω$-categories
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913394094768128 |
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| author | Benjamin, Thibaut Markakis, Ioannis |
| author_facet | Benjamin, Thibaut Markakis, Ioannis |
| contents | We study coinductive invertibility of cells in weak $ω$-categories. We use the inductive presentation of weak $ω$-categories via an adjunction with the category of computads, and show that invertible cells are closed under all operations of $ω$-categories. Moreover, we give a simple criterion for invertibility in computads, together with an algorithm computing the data witnessing the invertibility, including the inverse, and the cancellation data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invertible cells in $ω$-categories Benjamin, Thibaut Markakis, Ioannis Category Theory Logic in Computer Science We study coinductive invertibility of cells in weak $ω$-categories. We use the inductive presentation of weak $ω$-categories via an adjunction with the category of computads, and show that invertible cells are closed under all operations of $ω$-categories. Moreover, we give a simple criterion for invertibility in computads, together with an algorithm computing the data witnessing the invertibility, including the inverse, and the cancellation data. |
| title | Invertible cells in $ω$-categories |
| topic | Category Theory Logic in Computer Science |
| url | https://arxiv.org/abs/2406.12127 |