Steps toward the weak higher category of weak higher categories in the globular setting | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 3، دوره 4، شماره 1، اردیبهشت 2016، صفحه 9-42 اصل مقاله (597.29 K) | ||
| نوع مقاله: Research Paper | ||
| نویسنده | ||
| Camell Kachour* | ||
| Department of Mathematics, Macquarie University, North Ryde, NSW 2109, Australia. | ||
| چکیده | ||
| We start this article by rebuilding higher operads of weak higher transformations, and correct those in \cite{Cambat}. As in \cite{Cambat} we propose an operadic approach for weak higher $n$-transformations, for each $n\in\mathbb{N}$, where such weak higher $n$-transformations are seen as algebras for specific contractible higher operads. The last chapter of this article asserts that, up to precise hypotheses, the higher operad $B^{0}_{C}$ of Batanin and the terminal higher operad $B^{0}_{S_{u}}$, both have the fractal property. In other words we isolate the precise technical difficulties behind a major problem in globular higher category theory, namely, that of proving the existence of the globular weak higher category of globular weak higher categories. | ||
| کلیدواژهها | ||
| globular sets؛ weak higher categories؛ weak higher transformations؛ higher operads | ||
| مراجع | ||
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