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| Format: | Preprint |
| Publié: |
2022
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| Accès en ligne: | https://arxiv.org/abs/2210.07704 |
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| _version_ | 1866916416062488576 |
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| author | Araújo, Manuel |
| author_facet | Araújo, Manuel |
| contents | An $n$-sesquicategory is an $n$-globular set with strictly associative and unital composition and whiskering operations, which are however not required to satisfy the Godement interchange laws which hold in $n$-categories. In arXiv:2202.09293 we showed how these can be defined as algebras over a monad $T_n^{D^s}$ whose operations are simple string diagrams. In this paper, we give an explicit description of computads for the monad $T_n^{D^s}$ and we prove that the category of computads for this monad is a presheaf category. We use this to describe a string diagram notation for representing arbitrary composites in $n$-sesquicategories. This is a step towards a theory of string diagrams for semistrict $n$-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_07704 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Computads and string diagrams for $n$-sesquicategories Araújo, Manuel Category Theory 18N20, 18N30 An $n$-sesquicategory is an $n$-globular set with strictly associative and unital composition and whiskering operations, which are however not required to satisfy the Godement interchange laws which hold in $n$-categories. In arXiv:2202.09293 we showed how these can be defined as algebras over a monad $T_n^{D^s}$ whose operations are simple string diagrams. In this paper, we give an explicit description of computads for the monad $T_n^{D^s}$ and we prove that the category of computads for this monad is a presheaf category. We use this to describe a string diagram notation for representing arbitrary composites in $n$-sesquicategories. This is a step towards a theory of string diagrams for semistrict $n$-categories. |
| title | Computads and string diagrams for $n$-sesquicategories |
| topic | Category Theory 18N20, 18N30 |
| url | https://arxiv.org/abs/2210.07704 |