Priles of one-sided triangulated categories and exact model categories

2014/08/31 by Li, Zhi-Wei
#Algebraic Topology (math.AT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1409.0200

Abstract

We introduce the notion of a prile of one-sided triangulated categories. Roughly speaking, a prile consists of two one-sided triangulated categories having a common full subcategory which inherits a pretriangulated structure from these ambient categories. The main example arises from exact model categories. This allows us to recover the pretriangulated structure of the homotoy category of an exact model category.

Related

• Exact model structures and recollements
• A triangulated category without models
• A model category structure on the category of simplicial multicategories
• External triangulation of the homotopy category of exact quasi-category
• Closed Model Categories for Presheaves of Simplicial Groupoids and Presheaves of 2-Groupoids