\omega-Operads of coendomorphisms and fractal \omega-operads for higher structures

     In this article we introduce the notion of \textit{Fractal \omega-operad} emerging from  a natural \omega-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism \omega-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural \omega-operad acts on the globular object associated to these higher transformations. To construct the natural \omega-operad we introduce some general technology and give meaning to saying an \omega-operad possesses the \textit{fractal property}. If an \omega-operad B^{0}_{P} has this property then one can define a globular object of all higher B^{0}_{P}-transformations and show that the globular object has a B^{0}_{P}-algebra structure.

\omega-Operads of coendomorphisms and fractal \omega-operads for higher structures Keywords:

Higher categories , higher operads , weak higher transformations