2001/09/10 by Khaled Al-Takhman, Al-Takhman, Khaled
Mathematics · #16W30 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.QA #math.RA #msc:16W30
paper · pdf · doi:10.48550/arxiv.math/0109061
30 pages, xy-pic. To appear in Jornal of pure and applied algebra
arxiv created 2001/09/10 · openalex publication_date 2001/09/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we defined and studied quasi-finite comodules, the cohom functors for coalgebras over rings. linear functors between categories of comodules are also investigated and it is proved that good enough linear functors are nothing but a cotensor functor. Our main result of this work characterizes equivalences between comodule categories generalizing the Morita-Takeuchi theory to coalgebras over rings. Morita-Takeuchi contexts in our setting is defined and investigated, a correspondence between strict Morita-Takeuchi contexts and equivalences of comodule categories over the involved coalgebras is obtained. Finally we proved that for coalgebras over QF-rings Takeuchi's representation of the cohom-functor is also valid.