Università degli Studi di Genova

From cubical to globular higher categories
Abstract: We show that a strict symmetric (infinite-dimensional) cubical category A has an associated globular category Glb(A), consisting of its 'globular cubes'. The procedure of globularisation generally destroys important features of A, like the existence of limits and colimits or the presence of symmetries. Then we examine the much more complex weak case, up to constructing the tricategory associated to a weak symmetric 3-cubical category. Keywords: higher category, cubical category, globular category, symmetric cubical set, cospan. MSC: 18, 55 Pubblicato su: Diagrammes Vol. 67-68 suppl. (2012) Pag. 117-148

From cubical to globular higher categories