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

Format:

Book

Author/Creator:

Doherty, Brandon, author.

Kapulkin, Krzysztof, author.

Lindsey, Zachery, author.

Sattler, Christian, author.

Series:

Memoirs of the American Mathematical Society ; v. 1484.

Memoirs of the American Mathematical Society, 0065-9266 ; v. 1484

Language:

English

Subjects (All):

Geometry, Algebraic.

Categories (Mathematics).

Physical Description:

v, 110 pages : illustrations ; 26 cm.

Other Title:

Cubical models of (infinity, 1)-categories

Place of Publication:

Providence, RI : American Mathematical Society, 2024.

Summary:

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.

Contents:

Introduction

Chapter 1. Cubical sets and marked cubical sets

Chapter 2. Model structure on marked cubical sets

Chapter 3. Model structure on structurally marked cubical sets

Chapter 4. Joyal model structure on cubical sets

Chapter 5. Cones in cubical sets

Chapter 6. Comparison with the Joyal model structure

Chapter 7. Mapping spaces in cubical quasicategories

Appendix A. Verification of identities on.

Notes:

Includes bibliographical references (pages 109-110).

ISBN:

1470468948

9781470468941

OCLC:

1437986250