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

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• Globular weak $\omega$-categories as models of a type theory
• Note on the construction of globular weak omega-groupoids from types, topological spaces etc
• Aspects of Cubical Higher Category Theory
• Monoidal weak omega-categories as models of a type theory
• A Type Theory for Strictly Associative Infinity Categories
• Hom weak $\omega$-categories of a weak $\omega$-category
• Elimination of quotients in various localisations of premodels into models
• A semi-model structure for Grothendieck weak 3-groupoids