2008/08/31 by Julia Goedecke, Tim Van der Linden · 19 citations
Mathematics · #Abelian group #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Biology #Cellular homology #Gene #Genetics #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Spectral sequence #math.AT #math.CT #msc:18G #msc:20J #msc:55N40
paper · pdf · doi:10.1017/s0305004109990107
published in Mathematical Proceedings of the Cambridge Philosophical Society 147(3), 629-657 (Cambridge University Press) · 29 pages; major changes in Example 4.15, minor changes throughout the text
arxiv created 2009/03/06 · openalex publication_date 2009/06/22 · arxiv updated 2010/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract Working in a semi-abelian context, we use Janelidze's theory of generalised satellites to study universal properties of the Everaert long exact homology sequence. This results in a new definition of homology which does not depend on the existence of projective objects. We explore the relations with other notions of homology, and thus prove a version of the higher Hopf formulae. We also work out some examples.