Auslander--Iyama correspondence for exact dg categories

2023/08/16 by Xiaofa Chen, Chen, Xiaofa · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Applied mathematics #Category Theory (math.CT) #Exact solutions in general relativity #FOS: Mathematics #Generalization #Linguistics #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Philosophy #Representation Theory (math.RT) #Zero (linguistics)

paper · pdf · doi:10.48550/arxiv.2308.08519

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2023/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend Auslander--Iyama correspondence to the setting of exact dg categories. By specializing it to exact dg categories concentrated in degree zero, we obtain a generalization of the higher Auslander correspondence for exact categories due to Ebrahimi--Nasr-Isfahani (in the case of exact categories with split retractions).

Cited by

• A functorial approach to 0-abelian categories
• On the Auslander--Reiten Theory for Extended Hearts of Proper Connective DG Algebras

Related

• 0-Auslander correspondence
• Iyama-Solberg correspondence for exact dg categories
• Higher Auslander correspondence for exact categories
• Higher Auslander--Solberg correspondence for exact categories
• Exact dg categories II : The embedding theorem