  We introduce non-degenerate solutions of the Yang-Baxter equation in the
setting of symmetric monoidal categories. Our theory includes non-degenerate
set-theoretical solutions as basic examples. However, infinite families of
non-degenerate solutions (that are not of set-theoretical type) appear. As in
the classical theory of Etingof, Schedler and Soloviev, non-degenerate
solutions are classified in terms of invertible 1-cocycles. Braces and matched
pairs of cocommutative Hopf algebras (or braiding operators) are also
generalized to the context of symmetric monoidal categories and turn out to be
equivalent to invertible 1-cocycles.
