Note on Toda brackets

TL;DR

This paper generalizes Toda brackets within pointed model categories, illustrating their role as obstructions to rectification and linking them to classical stable operations, thus broadening their theoretical framework.

Contribution

It introduces a comprehensive definition of Toda brackets in model categories and explores their applications and connections to stable operations.

Findings

Toda brackets serve as obstructions to rectification.

The paper relates Toda brackets to classical stable operations.

Provides a unified framework for Toda brackets in model categories.

Abstract

We provide a general definition of Toda brackets in a pointed model categories, show how they serve as obstructions to rectification, and explain their relation to the classical stable operations.