We investigate the notion of involutive weak globular $omega$-categories via Jacque Penons 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.
