2006/01/24 by Matthew Grime, Grime, Matthew
Mathematics · #18G25 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.CT #math.RT #msc:18G25
paper · pdf · doi:10.48550/arxiv.math/0601575
20 pages. Added subsection on Transfer in the homotopy category, corrected typos (May 2006). Expanded to 20 pages, minor corrections, accepted for publication in Comm.in Alg. (August 2007)
openalex publication_date 2006/01/24 · arxiv created 2007/08/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a triple of functors. This includes the cases of homotopy and stable module categories. These categories naturally fit into a framework of relative derived categories, and once we prove that there are decent resolutions of complexes, we are able to prove many familiar results in homological algebra.