A cubical approach to straightening. Issue 4 (23rd October 2020)

• Record Type: Journal Article
• Authors: Kapulkin, Krzysztof; Voevodsky, Vladimir
• Is Part Of: Journal of topology. Volume 13:Issue 4(2020)
• Page Start: 1682
• Page End: 1700
• Publication Date: 2020-10-23
• Subjects: 55U35 (primary) -- 18G55 -- 55U40 (secondary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12173
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract: For a suitable choice of the cube category, we construct a Grothendieck topology on it such that sheaves with respect to this topology are exactly simplicial sets (thus establishing simplicial sets as a reflective subcategory of cubical sets). We then extend the construction of the homotopy coherent nerve to cubical categories and establish an analogue of Lurie's straightening–unstraightening construction.