Some Topics in coalgebra calculus

We study a coderivation from a cobimodule into a coalgebra. Vector cofields are defined by the action of a codual bicomodule on a coalgebra. This action is induced by a codifferential. A construction of a codual object in the category of bicomodules over a given coalgebra has been proposed. Various notions of duality have been analysed in this context.