Compatible weak factorization systems and model structures

2024/05/01 by Zhenxing Di, Liping Li, Di, Zhenxing +3
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2405.00312

openalex publication_date 2024/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 sSet) satisfy these conditions.

Related

• Weak model categories in classical and constructive mathematics
• Admissible weak factorization systems on extriangulated categories
• The nine model category structures on the category of sets
• Model structure from one hereditary complete cortorsion pair
• Factorization systems and double categories