Generalized Penon Involutive Weak Globular Higher Categories - Bejrakarbum, Paratat; Bertozzini, Paolo (Science & Technology Asia, 2024)
This research examines a generalization of the concept of an involutive weak globular 𝜔-category through Penon’s approach. We first introduce the notion of a globular cone, then equip it with compositions, identities, and self-duality. Next, a free reflexive self-dual globular-cone 𝜔-magma and a free strict involutive globular-cone 𝜔-category along with a specified contraction over a given globular cone are established. An algebra for the monad induced by the free-forgetful adjunction arising from the previously constructed structure naturally defines an involutive weak globular-cone 𝜔-category. We finally provide crucial examples of involutive weak globular-cone 𝜔-categories.