On comonadicity of the extension-of-scalars functors

Frobenius Extensions of Corings

Let $\Cc$ and $\Dd$ be two corings over a ring $A$ and $\Cc\stackrelλ{\longrightarrow}\Dd$ be a morphism of corings. We investigate the situation when the associated induced ("corestriction of scalars") functor $\Mm^\Cc\longrightarrow \Mm^\Dd$ is a Frobenius functor, and call these morphisms Frobenius extensions of corings. The characterization theorem generalizes notions such as Frobenius corings and is applied to several situations; in particular, provided some (general enough) flatness conditions hold, the notion proves to be dual to that of Frobenius extensions of rings (algebras). Several…

量子群余积与标量扩张下的普适性

Quantum group coproducts and universality under scalar extensions

本文刻画了域上双代数、Hopf代数及余代数族乘积有限维的条件，并纠正了标量扩张保持乘积的文献错误，明确了有限与代数扩张的普适性特征。