Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866918256419274752 |
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| author | Carranza, Daniel Kapulkin, Chris Wong, Liang Ze |
| author_facet | Carranza, Daniel Kapulkin, Chris Wong, Liang Ze |
| contents | The diagonal lemma asserts that if a map of bisimplicial sets is a levelwise weak equivalence in the Kan-Quillen model structure, then it induces a weak equivalence of the diagonal simplicial sets. In this short note, we observe that the standard proof of this fact works for an arbitrary Eilenberg-Zilber category in place of the simplex category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02217 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories Carranza, Daniel Kapulkin, Chris Wong, Liang Ze Algebraic Topology Category Theory 18N40, 55U35 (primary), 18N45, 18N50 (secondary) The diagonal lemma asserts that if a map of bisimplicial sets is a levelwise weak equivalence in the Kan-Quillen model structure, then it induces a weak equivalence of the diagonal simplicial sets. In this short note, we observe that the standard proof of this fact works for an arbitrary Eilenberg-Zilber category in place of the simplex category. |
| title | Diagonal Lemma for Presheaves on Eilenberg-Zilber Categories |
| topic | Algebraic Topology Category Theory 18N40, 55U35 (primary), 18N45, 18N50 (secondary) |
| url | https://arxiv.org/abs/2306.02217 |