2012/11/10 by Camell Kachour, Camell, Kachour
Mathematics · Medicine · #18F25 #18G55 #19M99 #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1211.2310
openalex publication_date 2012/11/10 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
It is well known that strict ω-categories, strict ω-functors, strict natural ω-transformations, and so on, form a strict ω-category. A similar property for weak ω-categories is one of the main hypotheses in higher category theory in the globular setting. In this paper we show that there is a natural globular ω-operad which acts on the globular set of weak ω-categories, weak ω-functors, weak natural ω-transformations, and so on. Thus to prove the hypothesis it remains to prove that this ω-operad is contractible in Batanin's sense. To construct such an ω-operad we introduce more general technology and suggest a definition of ω-operad with the fractal property. If an ω-operad B0P has this property then one can define a globular set of all higher B0P-transformations and, moreover, this globular set has a B0P-algebra structure.