2015/03/09 by Dimitri Ara, Ara, Dimitri, Georges Maltsiniotis +1
Mathematics · #18D05 #18G35 #18G55 #55P15 #55U10 #55U15 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1503.02720
openalex publication_date 2015/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is part of a series of papers about homotopy theory of strict n-categories. In the first paper of this series, we gave conditions that guarantee the existence of a Thomason model category structure on the category of strict n-categories. The main goal of our paper is to show one of these conditions. To do so, we associate to any simplicial complex a strict ∞-category generated by a computad. We conjecture that this ∞-category has the same homotopy type as the corresponding simplicial complex and we prove this conjecture when the simplicial complex comes from a poset. We introduce the notion of a quasi-initial object of an ∞-category and we show that Street's orientals admit such an object. One of the main tools used in this text is Steiner's theory of augmented directed complexes.