Globalizations for partial (co)actions on coalgebras

In this paper, we introduce the notion of globalization for partial module coalgebra and for partial comodule coalgebra. We show that every partial module coalgebra is globalizable exhibiting a standard globalization. We also show the existence of globalization for a partial comodule coalgebra, provided a certain rationality condition. Moreover, we show a relationship between the globalization for the (co)module coalgebra and the usual globalization for the (co)module algebra.