Equivalences of comodule categories for coalgebras over rings

✍ Scribed by Khaled Al-Takhman

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 260 KB
• Volume: 173
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(02)00013-0

✦ Synopsis

In this article we deÿned and studied quasi-ÿnite 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 deÿned 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.