Higher Structures, Vol. 4, No. 2, pp. 134-166, 2020
Polygraphs and discrete Conduché $\omega$-functors
Léonard Guetta
Received December 12th 2018. Published online June 30th 2020.
Abstract: We define a class of morphisms between strict $\omega$-categories called discrete Conduché $\omega$-functors that generalize discrete Conduché functors between categories and we study their properties related to polygraphs. The main result we prove is that for every discrete Conduché $\omega$-functor $f:C\rightarrow D$, if $D$ is a free strict $\omega$-category on a polygraph then so is $C$.
