Preresolving categories and derived equivalences

2020/10/25 by Ruben Henrard, Henrard, Ruben, Adam-Christiaan van Roosmalen +1
Mathematics · #18E05 #18G10 #18G80 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2010.13208

openalex publication_date 2020/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that a resolving subcategory A of an abelian subcategory E induces several derived equivalences: a triangle equivalence D^-(A)→ D^-(E) exists in general and furthermore restricts to a triangle equivalence D^b(A)→ D^b(E) if res.dim_A(E)

Citations

• Localizations of (one-sided) exact categories
• On topological cyclic homology

Related

• Relative Derived Category with respect to a Subcategory
• On derived categories and derived functors
• Lifting derived equivalences of abelian surfaces to generalized Kummer varieties
• Axiomatizing Subcategories of Abelian Categories
• Derived equivalences between subrings