Model category of marked objects

2016/10/26 by Valery Isaev, Isaev, Valery
Computer Science · Mathematics · #Category Theory (math.CT) #Constraint Satisfaction and Optimization #Data Management and Algorithms #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1610.08459

openalex publication_date 2016/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every functor F : K → C, where K is a small category and C is a model category which satisfies some mild hypotheses, we define a model category C^m of K-marked objects of C. We consider an application of this construction to the category of simplicial sets with the Joyal model structure. Marked simplicial sets can be thought of as (∞,1)-categories with some additional structure which depends on F. In particular, we construct a model category of quasi-categories which have limits of all diagrams of any given shape.

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