A cubical approach to straightening. Issue 4 (23rd October 2020) - Kapulkin, Krzysztof; Voevodsky, Vladimir
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.