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 $omega$-op...

‎in this article we discuss examples of fractal $omega$-operads‎. ‎thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{globular sets are also called $omega$-graphs by the french school.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma of...

we start this article by rebuilding higher operads of weak higher transformations, and correct those in cite{cambat}. as in cite{cambat} we propose an operadic approach for weak higher $n$-transformations, for each $ninmathbb{n}$, where such weak higher $n$-transformations are seen as algebras for specific contractible higher operads. the last chapter of this article asserts that, up to precise...

A general notion of operad is given, which includes: (1) the operads that arose in algebraic topology in the 1970’s to characterise loop spaces. (2) the higher operads of Michael Batanin [Bat98]. (3) braided and symmetric analogues of Batanin’s operads which are likely to be important in the study of weakly symmetric higher dimensional monoidal categories. The framework of this paper, links tog...

‎In this article we discuss examples of fractal $omega$-operads‎. ‎Thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma ...

     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 $omeg...