I List And I Die Hereditary

This dissertation consists of seven sections. We shall investigate descent theory of comodule.The first and second sections are introduction and preliminaries respectively.In the third section, we introduce the concepts of descent datum, right effective descentcoalgebra morphism etc., then we obtain an equivalence of categories Desc(C/B)≌M_A and some sufficient conditions that coalgebra morphismÏ€: C→B is right effective descent coalgcbra morphism.In the forth section, we introduce the concepts of descent datum, symmetries and connections associated to a comonad, and we obtain some bijeetions and an equivalence of categories Flconn≌Symm≌Desc.In the fifth section, we introduce a symmetric categoryX(G) associated to a comonad , and we have proofed that any morphism in this category is a morphism of comonad.In the sixth section, we introduce the concepts of Amitsur homology of a comonad and G forms, then we obtain two exact sequences and a bijeetion between Form(G, x₀) and Symrn(G(x₀)), where Form(G,x₀) denotes the set of isomorphism class G-form of x₀, and Syrnm(G(x₀)) denotes the set of all symmetries on G(x₀).In the seventh section, we apply some results into section 4 and section 6 to comodules, then we obtain the equivalences of categories Desc(C/B)≌M_A≌Flconn(C/B)≌Symm(C/B) and the following exact sequence:...