Compatible weak factorization systems and model structures
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914961644584960 |
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| author | Di, Zhenxing Li, Liping Liang, Li |
| author_facet | Di, Zhenxing Li, Liping Liang, Li |
| contents | In this paper the concept of compatible weak factorization systems in general categories is introduced as a counterpart of compatible complete cotorsion pairs in abelian categories. We describe a method to construct model structures on general categories via two compatible weak factorization systems satisfying certain conditions, and hence generalize a very useful result by Gillespie for abelian model structures. As particular examples, we show that weak factorizations systems associated to some classical model structures (for example, the Kan-Quillen model structure on $\mathsf{sSet}$) satisfy these conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compatible weak factorization systems and model structures Di, Zhenxing Li, Liping Liang, Li Category Theory Representation Theory In this paper the concept of compatible weak factorization systems in general categories is introduced as a counterpart of compatible complete cotorsion pairs in abelian categories. We describe a method to construct model structures on general categories via two compatible weak factorization systems satisfying certain conditions, and hence generalize a very useful result by Gillespie for abelian model structures. As particular examples, we show that weak factorizations systems associated to some classical model structures (for example, the Kan-Quillen model structure on $\mathsf{sSet}$) satisfy these conditions. |
| title | Compatible weak factorization systems and model structures |
| topic | Category Theory Representation Theory |
| url | https://arxiv.org/abs/2405.00312 |