Equivalences of comodule categories for coalgebras over rings |
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Authors: | Khaled Al-Takhman |
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Institution: | Department of Mathematics, Birzeit University, P.O. Box 14, Birzeit, Palestine |
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Abstract: | 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. |
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Keywords: | 16W30 |
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