  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.
