Involutive Weak Globular Higher Categories

Abstract

We investigate the notion of involutive weak globular $\omega$-categories via Jacque Penon's approach. In particular, we give the constructions of a free self-dual globular $\omega$-magma, of a free strict involutive globular $\omega$-category, over an $\omega$-globular set, and a contraction between them. The monadic definition of involutive weak globular $\omega$-categories is given as usual via algebras for the monad induced by a certain adjunction. In our case, the adjunction is obtained from the "free functor" that associates to every $\omega$-globular set the above contraction. Some examples of involutive weak globular $\omega$-categories are also provided.

14 pages, AMS-LaTeX2e. Reformatted version, only for arXiv purposes, of a paper submitted and published in the Proceedings of the "22nd Annual Meeting in Mathematics (AMM 2017)", 02-04 June 2017, Chiang Mai, Thailand