Operads of higher transformations for globular sets and for higher magmas

‎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 sets\footnote{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 reflexive \omega-magmas‎. ‎Thus‎, ‎even though the existence of the‎ ‎globular set of globular sets is intuitively evident‎, ‎many other higher structures which \textit{fractality} are less evident‎, ‎could be described‎ ‎with the same technology‎, ‎using fractal \omega-operads‎. ‎We have in mind the non-trivial question of the existence of the‎ ‎weak \omega-category of the weak \omega-categories in the globular setting‎, ‎which is described in \cite{kach-ir3} with the same technology up to a contractibility‎ ‎hypothesis‎.

Operads of higher transformations for globular sets and for higher magmas Keywords:

Higher categories , higher operads , weak higher transformations