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Cubical models of (∞,1)-categories / Brandon Doherty, Krzysztof Kapulkin, Zachery Lindsey, Christian Sattler.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 1484.Publisher: Providence, RI : American Mathematical Society, 2024Copyright date: ©2024Description: v, 110 pages : illustrations ; 26 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 1470468948
  • 9781470468941
Other title:
  • Cubical models of (infinity, 1)-categories
Subject(s): DDC classification:
  • D655c
Abstract: 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.
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Books Books Castorina Coleções de Monografias (Monographs Collections) Available 39063000809600

Includes bibliographical references (pages 109-110).

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.

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