Notes on $\omega$-graphs, reflexive $\omega$-graphs, their higher transformations, and $\omega$-operads

TL;DR

This paper introduces an $oldsymbol{ ext{ω}}$-operad framework to establish the existence of complex higher-dimensional graph structures, including reflexive variants, advancing the theoretical understanding of ω-graphs.

Contribution

It presents a novel $oldsymbol{ ext{ω}}$-operad approach to prove the existence of ω-graphs and reflexive ω-graphs, providing a new method in higher category theory.

Findings

Existence of ω-graph of ω-graphs established

Existence of reflexive ω-graph of reflexive ω-graphs proven

Operad-based method offers a new proof technique

Abstract

In this note we propose an $\omega$-operadical way to prove the existence of the $\omega$-graph of the $\omega$-graphs and the reflexive $\omega$- graph of the reflexive $\omega$-graphs.