Kachour, C. (2015). Operads of higher transformations for globular sets and for higher magmas. Categories and General Algebraic Structures with Applications, 3(1), 89-111.

Camell Kachour. "Operads of higher transformations for globular sets and for higher magmas". Categories and General Algebraic Structures with Applications, 3, 1, 2015, 89-111.

Kachour, C. (2015). 'Operads of higher transformations for globular sets and for higher magmas', Categories and General Algebraic Structures with Applications, 3(1), pp. 89-111.

Kachour, C. Operads of higher transformations for globular sets and for higher magmas. Categories and General Algebraic Structures with Applications, 2015; 3(1): 89-111.

Operads of higher transformations for globular sets and for higher magmas

^{}Department of Mathematics, Macquarie University, Sydney, Australia.

Abstract

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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