2014/02/18 by Anastasis Kratsios, Kratsios, Anastasis
Mathematics · #16T15 (Secondary) #18G10 (Primary) 13D03 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.CT #math.RA #msc:13D03 #msc:16T15 #msc:18G10
paper · pdf · doi:10.48550/arxiv.1402.4197
39 Pages
arxiv created 2014/02/18 · openalex publication_date 2014/02/18 · arxiv updated 2014/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of a duality between two derived functors as well as an extension theorem for derived functors to larger categories in which they need not be defined is introduced. These ideas are then applied to extend and study the coext functors to an arbitrary coalgebra. A new homology theory theory is then built therefrom and is shown to exhibit certain duality relations to the Hochschild cohomology of certain coalgebras. Lastly, a certain exceptional type of coalgebra is introduced and it is used to make explicit connections between this new homology theory and the continuous cohomology of this exceptional algebra's pro-finite dual algebra.