TY - JOUR ID - 10528 TI - Operads of higher transformations for globular sets and for higher magmas JO - Categories and General Algebraic Structures with Applications JA - CGASA LA - en SN - 2345-5853 AU - Kachour, Camell AD - Department of Mathematics, Macquarie University, Sydney, Australia. Y1 - 2015 PY - 2015 VL - 3 IS - 1 SP - 89 EP - 111 KW - Higher categories KW - higher operads KW - weak higher transformations DO - N2 - ‎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. UR - https://cgasa.sbu.ac.ir/article_10528.html L1 - https://cgasa.sbu.ac.ir/article_10528_b04f19db4ee999d77afc297225d3cf14.pdf ER -