Symmetric Cubical Sets

2009/10/26 by Samuel B. Isaacson, Isaacson, Samuel B.
Mathematics · #55u35 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0910.4948

openalex publication_date 2009/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new cubical model for homotopy types. More precisely, we'll define a category Qs with the following features: Qs is a PROP containing the classical box category as a subcategory, the category Qs-Set of presheaves of sets on Qs models the homotopy category, and combinatorial symmetric monoidal model categories with cofibrant unit all have homotopically well behaved Qs-Set enrichments.

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