Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 3 1 2015 07 01 $\omega$-Operads of coendomorphisms and fractal $\omega$-operads for higher structures 65 88 10527 EN Camell Kachour Department of Mathematics, Macquarie University, Sydney, Australia. Journal Article 2015 08 24      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. https://cgasa.sbu.ac.ir/article_10527_391dbbec71f3cd9c77ef8d4d484a2ed9.pdf