Polygraphs and Discrete Conduch{\'e} $\omega$-Functors

We define a class of morphisms between strict $\omega$-categories called discrete Conduch{'e} $\omega$-functors that generalize discrete Conduch{'e} functors between 1-categories and we study their properties related to polygraphs. The main result we prove is that for every discrete Conduch{'e} $\omega$-functor, if its target is a free strict $\omega$-category on a polygraph then so is its source.