Symmetric bimonoidal intermuting categories and $\omega\times\omega$ reduced bar constructions

TL;DR

This paper presents a new proof of coherence for categories with two symmetric monoidal structures connected by a natural transformation, enabling the construction of $oldsymbol{ ext{ extomega}} imes ext{ extomega}$-indexed iterated reduced bar constructions.

Contribution

It provides a self-contained proof of coherence for symmetric bimonoidal intermuting categories, facilitating advanced bar construction applications.

Findings

Coherence result established for categories with two symmetric monoidal structures.

Proof enables $ ext{ extomega} imes ext{ extomega}$-indexed iterated reduced bar constructions.

The approach is self-contained and simplifies previous coherence proofs.

Abstract

A new, self-contained, proof of a coherence result for categories equipped with two symmetric monoidal structures bridged by a natural transformation is given. It is shown that this coherence result is sufficient for $\omega\times\omega$-indexed family of iterated reduced bar constructions based on such a category.