2019/11/01 by Yasuaki Ogawa, Ogawa, Yasuaki
Mathematics · Physics and Astronomy · #18E10 #18E30 #18E35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1911.00259
openalex publication_date 2019/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of extriangulated category was introduced by Nakaoka and Palu giving a simultaneous generalization of exact categories and triangulated categories. Our first aim is to provide an extension to extriangulated categories of Auslander's formula: for some extriangulated category C, there exists a localization sequence defC\tomodC\tolexC, where lexC denotes the full subcategory of finitely presented left exact functors and defC the full subcategory of Auslander's defects. Moreover we provide a connection between the above localization sequence and the Gabriel-Quillen embedding theorem. As an application, we show that the general heart construction of a cotorsion pair (U,V) in a triangulated category, which was provided by Abe and Nakaoka, is same as the construction of a localization sequence defU\tomodU\tolexU.