Left determined model structures for locally presentable categories

2009/01/12 by Marc Olschok, Olschok, Marc
Mathematics · #18C35 #18G55 #55U35 #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.0901.1627

openalex publication_date 2009/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend a result of Cisinski on the construction of cofibrantly generated model structures from (Grothendieck) toposes to locally presentable categories and from monomorphism to more general cofibrations. As in the original case, under additional conditions, the resulting model structures are "left determined" in the sense of Rosicky and Tholen.

Citations

• The homotopy theory of equivalence relations

Related

• Minimal model structures
• Left-induced model structures and diagram categories
• From weak cofibration categories to model categories
• Grothendieck's Homotopy Hypothesis
• On (Enriched) Left Bousfield Localization of Model Categories