Let C be a coalgebra and let M be a right C-comodule. In this article we investigate the dimension of the space f of comodule morphisms from C to M. Our main result (Theorem 4) states that dim(∫M)≤dim(M), for every left co-Frobeuius coalgebra (with some additional properties) and for every finite dimensional right comodule M. In particular, taking M = ki we obtain