First, we present semisimple properties of twisted products by means of constructing an algebra isomorphism between twisted products and crossed products, and point out that there exist some relations among braided bialgebras, paired bialgebras and Yang-Baxter coalgebras. Furthermore, we give an example to illustrate these relations by using Sweedler's 4-dimensional Hopf algebra. Finally, from starting off with Yang-Baxter coalgebras, we can construct some quadratic bialgebras such that they are braided bialgebras.
