2021/10/31 by Cottrell, Thomas, Fujii, Soichiro
#18N20 #18N65 #Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2111.00439
Classical definitions of weak higher-dimensional categories are given inductively; for example, a bicategory has a set of objects and hom categories, and a tricategory has a set of objects and hom bicategories. However, more recent definitions of weak n-categories for all natural numbers n, or of weak ω-categories, take more sophisticated approaches, and the nature of the "hom" is often not immediate from the definitions. In this paper, we focus on Leinster's definition of weak ω-category based on an earlier definition by Batanin, and construct for each weak ω-category A, an underlying (weak ω-category)-enriched graph consisting of the same objects and for each pair of objects x and y, a hom weak ω-category A(x,y). We also show that our construction is functorial with respect to weak ω-functors introduced by Garner.