2013/10/31 by Daniel R. Grayson, Grayson, Daniel R. · 1 citation
Mathematics · #19 #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1310.8644
openalex publication_date 2013/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous paper I gave a presentation for the Quillen higher algebraic K-groups of an exact category in terms of "acyclic binary multicomplexes". In this paper I take that presentation as a definition of the higher K-groups, generalize it to the relative K-groups of an exact functor between exact categories, and produce the corresponding long exact sequence by elementary means, without homotopy theory.