String Diagrams for Premonoidal Categories
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913821195501568 |
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| author | Román, Mario Sobociński, Paweł |
| author_facet | Román, Mario Sobociński, Paweł |
| contents | Premonoidal categories are monoidal categories without the interchange law while effectful categories are premonoidal categories with a chosen monoidal subcategory of interchanging morphisms. In the same sense that string diagrams, pioneered by Joyal and Street, are an internal language for monoidal categories, we show that string diagrams with an added "runtime object", pioneered by Alan Jeffrey, are an internal language for effectful categories and can be used as string diagrams for effectful, premonoidal, and Freyd categories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_06075 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | String Diagrams for Premonoidal Categories Román, Mario Sobociński, Paweł Category Theory 18M30 Premonoidal categories are monoidal categories without the interchange law while effectful categories are premonoidal categories with a chosen monoidal subcategory of interchanging morphisms. In the same sense that string diagrams, pioneered by Joyal and Street, are an internal language for monoidal categories, we show that string diagrams with an added "runtime object", pioneered by Alan Jeffrey, are an internal language for effectful categories and can be used as string diagrams for effectful, premonoidal, and Freyd categories. |
| title | String Diagrams for Premonoidal Categories |
| topic | Category Theory 18M30 |
| url | https://arxiv.org/abs/2305.06075 |