The cube axiom and resolutions in homotopy theory

TL;DR

This paper demonstrates a version of the cube axiom in cosimplicial unstable coalgebras and spaces, extending classical unstable homotopy theory results through a resolution model structure.

Contribution

It introduces a new version of the cube axiom in cosimplicial contexts and applies it to extend classical theorems in unstable homotopy theory.

Findings

Cube axiom holds in cosimplicial unstable coalgebras and spaces.

Classical theorems are extended to these cosimplicial settings.

Resolution model structures facilitate these extensions.

Abstract

We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model structure. As an application, classical theorems in unstable homotopy theory are extended to this context.