Homological coalgebra

Abstract

The purpose of this paper is to give an introduction to the homological theory of comodules over coalgebras and Hopf algebras. Section 1 is a self- contained exposition of basic concepts such as cotensor product, injective comodules and change of coalgebras. Some results analogous to the results , Hochschild [5]) on rational modules over affine algebraic groups are proved. S ection 2 deals with the representation theory of co-Fro- benius coalgebras and coseparable coalgebras. We reproduce in this section some of Lin's results