TY - JOUR
ID - 11180
TI - Steps toward the weak higher category of weak higher categories in the globular setting
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Kachour, Camell
AD - Department of Mathematics, Macquarie University, North Ryde, NSW 2109, Australia.
Y1 - 2016
PY - 2016
VL - 4
IS - 1
SP - 9
EP - 42
KW - globular sets
KW - weak higher categories
KW - weak higher transformations
KW - higher operads
DO -
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_11180.html
L1 - https://cgasa.sbu.ac.ir/article_11180_b13cacfd9afe5780932141c269d0add6.pdf
ER -