Constructing the Cocyclic Structures for Crossed Coproduct Coalgebras

Abstract

In this paper, we construct a cocylindrical object associated to two coalgebras and a cotwisted map. It is shown that there exists an isomorphism between the cocyclic object of the crossed coproduct coalgebra induced from two coalgebras with a cotwisted map and the cocyclic object related to the diagonal of the cocylindrical object.