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Title: Equivalences of comodule categories for coalgebras over rings
Authors: Al-Takhman, Khaled 
Keywords: Duality theory (Mathematics);Quasi-finite comodules
Issue Date: 2002
Publisher: Journal of Pure and Applied Algebra
Abstract: In this article we defined and studied the quasi-finite comodules, 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 de2ned 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 cohomfunctor is also valid.
DOI: 10.1016/S0022-4049(02)00013-0
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