nLab
omega-groupoid

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Idea

An ω\omega-groupoid is an ω-category (see there for more details) in which all k-morphisms for all kk \in \mathbb{N} are equivalences.

This is also called an ∞-groupoid. In the literature the term “ω\omega-groupoid” is usually reserved for algebraic models instead of geometric models.

How strict the ω\omega-category and the inverses must be can vary. Somes authors that use the term ‘ω\omega-groupoid’ mean strict ω-groupoid by default and speak of weak ω\omega-groupoid otherwise.

Revised on November 6, 2014 17:15:49 by Urs Schreiber (81.194.35.225)