Computads for weak $ω$-categories as an inductive type
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909377223458816 |
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| author | Dean, Christopher J. Finster, Eric Markakis, Ioannis Reutter, David Vicary, Jamie |
| author_facet | Dean, Christopher J. Finster, Eric Markakis, Ioannis Reutter, David Vicary, Jamie |
| contents | We give a new description of computads for weak globular $ω$-categories by giving an explicit inductive definition of the free words. This yields a new understanding of computads, and allows a new definition of $ω$-category that avoids the technology of globular operads. Our framework permits direct proofs of important results via structural induction, and we use this to give new proofs that every $ω$-category is equivalent to a free one, and that the category of computads with generator-preserving maps is a presheaf topos, giving a direct description of the index category. We prove that our resulting definition of $ω$-category agrees with that of Batanin and Leinster and that the induced notion of cofibrant replacement for $ω$-categories coincides with that of Garner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_08719 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Computads for weak $ω$-categories as an inductive type Dean, Christopher J. Finster, Eric Markakis, Ioannis Reutter, David Vicary, Jamie Category Theory We give a new description of computads for weak globular $ω$-categories by giving an explicit inductive definition of the free words. This yields a new understanding of computads, and allows a new definition of $ω$-category that avoids the technology of globular operads. Our framework permits direct proofs of important results via structural induction, and we use this to give new proofs that every $ω$-category is equivalent to a free one, and that the category of computads with generator-preserving maps is a presheaf topos, giving a direct description of the index category. We prove that our resulting definition of $ω$-category agrees with that of Batanin and Leinster and that the induced notion of cofibrant replacement for $ω$-categories coincides with that of Garner. |
| title | Computads for weak $ω$-categories as an inductive type |
| topic | Category Theory |
| url | https://arxiv.org/abs/2208.08719 |