Operads of higher transformations for globular sets and for higher magmas

Document Type: Research Paper


Department of Mathematics, Macquarie University, Sydney, Australia.


‎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.


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