Doherty, Brandon, <br/><br/>
Cubical models of (&#x221E;,1)-categories / 
 Cubical models of (infinity, 1)-categories 
Brandon Doherty, Krzysztof Kapulkin, Zachery Lindsey, Christian Sattler. 
 - v, 110 pages :  illustrations ;  26 cm. 
 - Memoirs of the American Mathematical Society,  v. 1484  0065-9266 ; .
 - Memoirs of the American Mathematical Society ;  v. 1484. .
<br/><br/>Includes bibliographical references (pages 109-110). 
<br/><br/> We construct a model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical analogue of inner horns. We show that this model structure is Quillen equivalent to the Joyal model structure on simplicial sets via the triangulation functor. As an application, we show that cubical quasicategories admit a convenient notion of a mapping space, which we use to characterize the weak equivalences between fibrant objects in our model structure as DK-equivalences. 
<br/><br/><label>ISBN: </label>1470468948 9781470468941 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Geometry, Algebraic.<br/>Categories (Mathematics)
<br/><br/><label>Dewey Class. No.: </label> / D655c