Bonjour, Let us call cubical omega-category a cubical complex with connections and operations +_j like in the paper "On the algebra of cube", Brown & Higgins or like in Al-Agl's PhD "Aspect of multiple categories". There is a conjecture which claims that the category of cubical omega-categories is equivalent to the category of globular omega-categories. If I understand correctly, the conjecture was proved in some richer framework but seems to be (in my knowledge) still open as stated above. My question is : is there a similar conjecture for weak omega-category ? Is there a notion of cubical weak omega-category somewhere in the literature and a notion of globular weak omega-category ? Any reference is welcome. I have found nothing with the usual research engine but maybe I did not use the good key-word. pg.