# Steps toward the weak higher category of weak higher categories in the globular setting

Document Type : Research Paper

Author

Department of Mathematics, Macquarie University, North Ryde, NSW 2109, Australia.

Abstract

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.

Keywords

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