An infinity operad of normalized cacti

TL;DR

This paper demonstrates that normalized cacti can be structured as an infinity-operad within dendroidal spaces, introducing a new topological operad and enriching the dendroidal category to achieve this.

Contribution

It introduces a novel topological operad of bracketed trees and enriches the dendroidal category to establish normalized cacti as an infinity-operad.

Findings

Normalized cacti form an infinity-operad in dendroidal spaces.

A new topological operad of bracketed trees is constructed.

Enrichment of the dendroidal category $oldsymbol{ ext{Ω}}$ is developed.

Abstract

We show that normalized cacti form an $\infty$-operad in the form of a dendroidal space satisfying a weak Segal condition. To do this, we introduce a new topological operad of bracketed trees and an enrichment of the dendroidal category $\Omega$.