%0 Journal Article
%T Steps toward the weak higher category of weak higher categories in the globular setting
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Kachour, Camell
%D 2016
%\ 02/01/2016
%V 4
%N 1
%P 9-42
%! Steps toward the weak higher category of weak higher categories in the globular setting
%K globular sets
%K weak higher categories
%K weak higher transformations
%K higher operads
%R
%X 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.
%U https://cgasa.sbu.ac.ir/article_11180_b13cacfd9afe5780932141c269d0add6.pdf