Weak braided monoidal categories and their homotopy colimits

TL;DR

This paper demonstrates that the homotopy colimit construction for diagrams of weak braided monoidal categories accurately captures the intended homotopy type, enabling a flexible categorical realization of E-2 spaces.

Contribution

It extends the homotopy colimit construction to weak braided monoidal categories, enhancing categorical models of E-2 spaces.

Findings

Homotopy colimit construction correctly models the homotopy type for weak braided monoidal categories.

Provides a flexible categorical framework for realizing E-2 spaces.

Extends previous work to a broader class of monoidal categories.

Abstract

We show that the homotopy colimit construction for diagrams of categories with an operad action, recently introduced by Fiedorowicz, Stelzer and Vogt, has the desired homotopy type for diagrams of weak braided monoidal categories. This provides a more flexible way to realize E-2 spaces categorically.