Polygraphs and Discrete Conduch{é} $\omega$-Functors

Abstract

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