Involutive Weak Cubical ω-categories

2025/05/20 by Bejrakarbum, Paratat, Bertozzini, Paolo, Theesoongnern, Supaporn
#18M40 #18N30 #18N65 (Primary) 18N70 #18N99 (Secondary) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.13850

Abstract

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

Citations

• On Strict Higher C*-categories
• Multiple categories: the equivalence of a globular and a cubical approach

Related

• Aspects of Cubical Higher Category Theory
• Involutive Weak Globular Higher Categories
• Involutive Weak Globular ω-categories
• Cubical (omega,p)-categories
• Combinatorial approach to the category Θ₀ of cubical pasting diagrams