2022/08/28 by Henrik Holm, Holm, Henrik, Peter Jørgensen +1 · 1 citation
Mathematics · #16E35 #18G80 #18N40 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2208.13282
openalex publication_date 2022/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous work we constructed the Q-shaped derived category of any ring A for any suitably nice category Q. The Q-shaped derived category of A, which is denoted by DQ(A), is a generalization of the ordinary derived category. In this paper we prove that the Q-shaped derived category of A is a compactly generated triangulated category. We also define perfect objects in DQ(A) and prove that these constitute a triangulated subcategory, DperfQ(A), of the category DQ(A)c of compact objects in the Q-shaped derived category. The subcategories DperfQ(A) and DQ(A)c coincide if and only if the former is thick.