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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.20555 |
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| _version_ | 1866908558956691456 |
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| author | Leinster, Tom |
| author_facet | Leinster, Tom |
| contents | Many types of categorical structure obey the following principle: the natural notion of equivalence is generated, as an equivalence relation, by identifying $A$ with $B$ when there exists a strictly structure-preserving map $A \to B$ that is genuinely (not just essentially) surjective in each dimension and faithful in the top dimension. We prove this principle for four types of structure: categories, monoidal categories, bicategories and double categories. The last of these theorems suggests that the right notion of equivalence between double categories is Campbell's gregarious double equivalence, a conclusion also reached for different reasons in recent work of Moser, Sarazola and Verdugo. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20555 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivalence via surjections Leinster, Tom Category Theory Many types of categorical structure obey the following principle: the natural notion of equivalence is generated, as an equivalence relation, by identifying $A$ with $B$ when there exists a strictly structure-preserving map $A \to B$ that is genuinely (not just essentially) surjective in each dimension and faithful in the top dimension. We prove this principle for four types of structure: categories, monoidal categories, bicategories and double categories. The last of these theorems suggests that the right notion of equivalence between double categories is Campbell's gregarious double equivalence, a conclusion also reached for different reasons in recent work of Moser, Sarazola and Verdugo. |
| title | Equivalence via surjections |
| topic | Category Theory |
| url | https://arxiv.org/abs/2508.20555 |