Picard groups for graded coalgebras (original) (raw)

This paper introduces group invariants for graded coalgebras, specifically focusing on the category of graded comodules. It establishes that the category of graded comodules over a G-graded coalgebra is isomorphic to that over the smash coproduct with a group algebra. The notion of graded equivalence is introduced, leading to the construction of a graded Picard group that characterizes these equivalences. The study also applies Morita-Takeuchi theory to derive new examples of the standard Picard group of coalgebras.