On categories with arbitrary 2-cell structures
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911914495311872 |
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| author | Martins-Ferreira, Nelson |
| author_facet | Martins-Ferreira, Nelson |
| contents | When a category is equipped with a 2-cell structure it becomes a sesquicategory but not necessarily a 2-category. It is widely accepted that the latter property is equivalent to the middle interchange law. However, little attention has been given to the study of the category of all 2-cell structures (seen as sesquicategories with a fixed underlying base category) other than as a generalization for 2-categories. The purpose of this work is to highlight the significance of such a study, which can prove valuable in identifying intrinsic features pertaining to the base category. These ideas are expanded upon through the guiding example of the category of monoids. Specifically, when a monoid is viewed as a one-object category, its 2-cell structures resemble semibimodules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On categories with arbitrary 2-cell structures Martins-Ferreira, Nelson Category Theory 18N10, 18N20, 16D20 When a category is equipped with a 2-cell structure it becomes a sesquicategory but not necessarily a 2-category. It is widely accepted that the latter property is equivalent to the middle interchange law. However, little attention has been given to the study of the category of all 2-cell structures (seen as sesquicategories with a fixed underlying base category) other than as a generalization for 2-categories. The purpose of this work is to highlight the significance of such a study, which can prove valuable in identifying intrinsic features pertaining to the base category. These ideas are expanded upon through the guiding example of the category of monoids. Specifically, when a monoid is viewed as a one-object category, its 2-cell structures resemble semibimodules. |
| title | On categories with arbitrary 2-cell structures |
| topic | Category Theory 18N10, 18N20, 16D20 |
| url | https://arxiv.org/abs/2406.08240 |