$\omega$-Operads of coendomorphisms and fractal $\omega$-operads for higher structures | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 5، دوره 3، شماره 1، مهر 2015، صفحه 65-88 اصل مقاله (1.85 M) | ||
| نوع مقاله: Research Paper | ||
| نویسنده | ||
| Camell Kachour* | ||
| Department of Mathematics, Macquarie University, Sydney, Australia. | ||
| چکیده | ||
| In this article we introduce the notion of \textit{Fractal $\omega$-operad} emerging from a natural $\omega$-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism $\omega$-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural $\omega$-operad acts on the globular object associated to these higher transformations. To construct the natural $\omega$-operad we introduce some general technology and give meaning to saying an $\omega$-operad possesses the \textit{fractal property}. If an $\omega$-operad $B^{0}_{P}$ has this property then one can define a globular object of all higher $B^{0}_{P}$-transformations and show that the globular object has a $B^{0}_{P}$-algebra structure. | ||
| کلیدواژهها | ||
| Higher categories؛ higher operads؛ weak higher transformations | ||
| مراجع | ||
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