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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.02607 |
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| _version_ | 1866912625631166464 |
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| author | Martínez, César Bardomiano Henry, Simon |
| author_facet | Martínez, César Bardomiano Henry, Simon |
| contents | We attach to each weak model category $\mathcal{M}$ a class of first order formulas about the fibrant objects of $\mathcal{M}$ whose validity is invariant under homotopies and weak equivalences. This is a generalization of the classical Blanc-Freyd Language of categories -- which involves formula avoiding equality on objects and which are invariant under isomorphism and equivalences of categories. In particular, we obtain similar homotopy invariant languages for $2$-categories, bicategories, chain complexes, Kan complexes, quasi-categories, Segal spaces, and so on... |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homotopy Languages Martínez, César Bardomiano Henry, Simon Category Theory Algebraic Topology Logic 18A15, 18C10, 18N40, 18N45, 55U35 We attach to each weak model category $\mathcal{M}$ a class of first order formulas about the fibrant objects of $\mathcal{M}$ whose validity is invariant under homotopies and weak equivalences. This is a generalization of the classical Blanc-Freyd Language of categories -- which involves formula avoiding equality on objects and which are invariant under isomorphism and equivalences of categories. In particular, we obtain similar homotopy invariant languages for $2$-categories, bicategories, chain complexes, Kan complexes, quasi-categories, Segal spaces, and so on... |
| title | Homotopy Languages |
| topic | Category Theory Algebraic Topology Logic 18A15, 18C10, 18N40, 18N45, 55U35 |
| url | https://arxiv.org/abs/2510.02607 |