(untitled) (Journal of Mathematical Study, 2022)
Let C be a coalgebra. We prove that a right C-comodule is an n-cosyzygy if and only if it is a Gorenstein n-cosyzygy. We study the Gorenstein global dimension of coalgebras and the class of Gorenstein hereditary coalgebras. As a generalization of Gorenstein hereditary coalgebras, we introduce the concept of Gorenstein semihereditary coalgebras and show that a coalgebra C is Gorenstein semihereditary if and only if every finitely cogenerated factor of any injective comodule is Gorenstein injective.