On Algebraic Models for Homotopy 3-Types

TL;DR

This paper investigates the relationships between various algebraic models used to represent homotopy 3-types, aiming to unify and clarify their connections.

Contribution

It provides a detailed analysis of the connections among quadratic modules, 2-crossed modules, crossed squares, and simplicial groups with Moore complex of length 2.

Findings

Established equivalences among different algebraic models for homotopy 3-types

Clarified the structural relationships between quadratic modules and simplicial groups

Enhanced understanding of algebraic representations of homotopy 3-types

Abstract

We explore the relations among quadratic modules, 2-crossed modules, crossed squares and simplicial groups with Moore complex of length 2.