Involutive Weak Cubical $\omega$-categories

TL;DR

This paper explores involutive weak cubical omega-categories using Penon's approach, defining them as algebras for a specific monad and providing examples to illustrate their structure.

Contribution

It introduces a novel framework for involutive weak cubical omega-categories via monads, expanding the understanding of their algebraic structure.

Findings

Defined involutive weak cubical omega-categories as monad algebras

Provided examples of involutive weak cubical omega-categories

Extended the theoretical framework for cubical omega-categories

Abstract

We investigate the notion of involutive weak cubical $\omega$-categories via Penon's approach: as algebras for the monad induced by the free involutive strict $\omega$-category functor on cubical $\omega$-sets. A few examples of involutive weak cubical $\omega$-categories are provided.