Grothendieck $\mathrm{\infty }$-groupoids, and still another definition of $\mathrm{\infty }$-categories

The aim of this paper is to present a simplified version of the notion of $\mathrm{\infty }$-groupoid developed by Grothendieck in “Pursuing Stacks” and to introduce a definition of $\mathrm{\infty }$-categories inspired by Grothendieck’s approach.