Abstract
ABSTRACT A pair of adjoint functors is called a Frobenius pair of the second type if is a left adjoint of for some category equivalences and . Frobenius ring extensions of the second kind provide examples of Frobenius pairs of the second kind. We study Frobenius pairs of the second kind between categories of modules, comodules, and comodules over a coring. We recover the result that a finitely generated projective Hopf algebra over a commutative ring is always a Frobenius extension of the second kind (cf.[27], [17], and prove that the integral spaces of the Hopf algebra and its dual are isomorphic.
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