Weak braided Hopf algebras J. N. Alonso AlvarezJ. M. Fernandez VilaboaR. Gonzalez Rodriguez 16W3018D10weak Yang-Baxter operatorweak braided Hopf algebraYetter-Drinfeld moduleHopf module In this paper we give an introduction to the theory of weak braided Hopf algebras proposed as a braided version of weak Hopf algebras. Also, we obtain the fundamental theorem of Hopf modules for these algebraic structures. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3294 10.1512/iumj.2008.57.3294 en Indiana Univ. Math. J. 57 (2008) 2423 - 2458 state-of-the-art mathematics http://iumj.org/access/