2004/07/02 by Hans Joachim Baues, Baues, Hans Joachim, Mamuka Jibladze +1
Mathematics · Medicine · #18D05 #18G10 #18G25 #18G40 (Secondary) #55S20 (Primary) 55U99 #55T15 #Algebraic Topology (math.AT) #Cancer Treatment and Pharmacology #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AT #math.CT #math.KT #msc:18D05 #msc:18G10 #msc:18G25 #msc:18G40 #msc:55S20 #msc:55T15 #msc:55U99
paper · pdf · doi:10.48550/arxiv.math/0407031
Reference to math.AT/0407045 added
openalex publication_date 2004/07/02 · arxiv created 2004/07/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Classical homological algebra takes place in additive categories. In homotopy theory such additive categories arise as homotopy categories of ``additive groupoid enriched categories'', in which a secondary analog of homological algebra can be performed. We introduce secondary chain complexes and secondary resolutions leading to the concept of secondary derived functors. As a main result we show that the E3-term of the Adams spectral sequence can be expressed as a secondary derived functor. This result can be used to compute the E3-term explicitly by an algorithm.