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

TL;DR

This paper simplifies Grothendieck's concept of infinity-groupoids and introduces a new definition of infinity-categories inspired by his approach, aiming to clarify and unify higher categorical structures.

Contribution

It provides a streamlined version of Grothendieck's infinity-groupoids and proposes a novel definition of infinity-categories based on his ideas.

Findings

Simplified the notion of infinity-groupoids

Introduced a new approach to defining infinity-categories

Bridged concepts between infinity-groupoids and infinity-categories

Abstract

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