Operads of higher transformations for globular sets and for higher magmas | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 6، دوره 3، شماره 1، مهر 2015، صفحه 89-111 اصل مقاله (1.86 M) | ||
| نوع مقاله: Research Paper | ||
| نویسنده | ||
| Camell Kachour* | ||
| Department of Mathematics, Macquarie University, Sydney, Australia. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Higher categories؛ higher operads؛ weak higher transformations | ||
| مراجع | ||
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