Double categorical equivalences
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912611654696960 |
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| author | Moser, Lyne Sarazola, Maru Verdugo, Paula |
| author_facet | Moser, Lyne Sarazola, Maru Verdugo, Paula |
| contents | We present an efficient and user-friendly method for constructing any cofibrantly generated model structure on the category of double categories whose trivial fibrations are the "canonical" ones: the double functors which are surjective on objects, full on both horizontal and vertical morphisms, and fully faithful on squares. We show that all of these model structures are left proper and that they are localizations of the gregarious model structure introduced by Campbell. As a notable consequence, this identifies the gregarious weak equivalences as the "canonical" equivalences of double categories, an elusive notion thus far. Moreover, the nature of our method gives an explicit description of the fibrant objects in terms of lifting conditions. We use this to recover several known model structures, as well as construct several new examples whose homotopy theories encode a range of $2$-dimensional structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23181 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Double categorical equivalences Moser, Lyne Sarazola, Maru Verdugo, Paula Algebraic Topology Category Theory 18N10, 18N40, 18D40, 55U35 We present an efficient and user-friendly method for constructing any cofibrantly generated model structure on the category of double categories whose trivial fibrations are the "canonical" ones: the double functors which are surjective on objects, full on both horizontal and vertical morphisms, and fully faithful on squares. We show that all of these model structures are left proper and that they are localizations of the gregarious model structure introduced by Campbell. As a notable consequence, this identifies the gregarious weak equivalences as the "canonical" equivalences of double categories, an elusive notion thus far. Moreover, the nature of our method gives an explicit description of the fibrant objects in terms of lifting conditions. We use this to recover several known model structures, as well as construct several new examples whose homotopy theories encode a range of $2$-dimensional structures. |
| title | Double categorical equivalences |
| topic | Algebraic Topology Category Theory 18N10, 18N40, 18D40, 55U35 |
| url | https://arxiv.org/abs/2509.23181 |