Coherence for invertible objects and multi-graded homotopy rings

TL;DR

This paper establishes a coherence theorem for invertible objects in symmetric monoidal categories, enabling the derivation of algebraic properties for multi-graded homotopy rings, thus generalizing classical results in stable homotopy theory.

Contribution

It introduces a coherence theorem for invertible objects, facilitating new algebraic structures and properties in multi-graded homotopy rings within symmetric monoidal categories.

Findings

Proves a coherence theorem for invertible objects.

Derives associativity and skew-commutativity for multi-graded rings.

Generalizes classical stable homotopy group results.

Abstract

We prove a coherence theorem for invertible objects in a symmetric monoidal category. This is used to deduce associativity, skew-commutativity, and related results for multi-graded morphism rings, generalizing the well-known versions for stable homotopy groups.