Frobenius and Separable Functors for Generalized Module Categories and Nonlinear Equations (Lecture Notes in Mathematics) - Info and Reading Options

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Intro -- 1 Generalities -- 1.1 Coalgebras, bialgebras, and Hopf algebras -- Algebras and coalgebras -- The convolution product -- Bialgebras and Hopf algebras -- Modules -- Module algebras and module coalgebras -- Comodules -- The cotensor product -- Coflatness versus injectivity -- Comodule algebras and comodule coalgebras -- 1.2 Adjoint functors -- Pairs of adjoint functors -- 1.3 Separable algebras and Frobenius algebras -- Separable algebras -- Frobenius algebras -- The problem of Frobenius -- 2 Doi-Koppinen Hopf modules and entwined modules -- 2.1 Doi-Koppinen structures and entwining structures -- Entwining structures -- Doi-Koppinen structures -- Alternative Doi-Koppinen structures -- Doi-Koppinen structures versus entwining structures -- 2.2 Doi-Koppinen modules and entwined modules -- Entwined modules -- Doi-Koppinen Hopf modules -- 2.3 Entwined modules and the smash product -- Koppinen's smash product -- 2.4 Entwined modules and the smash coproduct -- 2.5 Adjoint functors for entwined modules -- 2.6 Two-sided entwined modules -- 2.7 Entwined modules and comodules over a coring -- 2.8 Monoidal categories -- 3 Frobenius and separable functors for entwined modules -- 3.1 Separable functors and Frobenius functors -- Frobenius functors -- Separable functors and Maschke's Theorem -- Relative injective and projective objects -- Separable functors of the second kind -- Fully faithful functors -- 3.2 Restriction of scalars and the smash product -- Application to the smash product -- Application to Hopf algebras -- Frobenius modules and Λ-separability -- 3.3 The functor forgetting the C-coaction -- Relative separability -- 3.4 The functor forgetting the A-action -- 3.5 The general induction functor -- T-generators -- Separability of F -- Separability of the adjoint of the induction functor -- 4 Applications -- 4.1 Relative Hopf modules

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