Involutive Weak Globular Higher Categories

الأصل · EN

We investigate the notion of involutive weak globular ω-categories via Jacque Penon's approach. In particular, we give the constructions of a free self-dual globular ω-magma, of a free strict involutive globular ω-category, over an ω-globular set, and a contraction between them. The monadic definition of involutive weak globular ω-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 ω-globular set the above contraction. Some examples of involutive weak globular ω-categories are also provided.