Operadic Definition of Non-Stricts Cells

In [K. Kachour. D'efinition alg'ebrique des cellules non-strictes. Cahiers de Topologie et de G'eom'etrie Diff'erentielle Cat'egorique, 1:1-68, 2008] we pursue Penon’s work in higher dimensional categories by defining non-strict infinity-functors, non-strict natural infinity-transformations, and so on, all that with Penon’s frameworks i.e with the “'etirements cat'egoriques”, where we have used an extension of this object, namely the “n-'etirements cat'egoriques” (n belong in N). In this paper we are pursuing Batanin’s work in higher dimensional categories by defining nonstrict infinity-functors, non-strict natural infinity-transformations, and so on, using Batanin’s frameworks i.e with the contractible operads, where we used an extension of this object, namely the globular colored contractible operads.