Year: 2025
Type: article
Abstract: We use Cisinski's machinery to construct and study model structures on the category of simplicial sets whose classes of fibrant objects generalize quasicategories.We identify a lifting condition that captures the homotopical behavior of quasicategories without the algebraic aspects and show that there is a model structure whose fibrant objects are precisely those that satisfy this condition.We also identify a localization of this model structure whose fibrant objects satisfy a "special horn lifting" property similar to the one satisfied by quasicategories.This special horn model structure leads to a conjectural characterization of the bijective-on-0-simplices trivial cofibrations of the Joyal model structure.We also discuss how these model structures all relate to one another and to the minimal model structure.18N50, 55U35; 18N60 1. Introduction 357 2. Background 362 3. Homotopically behaved model structures and augmented horns 365 4. Minimal homotopically behaved model structures 373 5.A model structure for special horn inclusions 388 6. Comparing model structures 394
Source: Algebraic & Geometric Topology
Author: Matt Feller
Institution: University of Virginia
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: National Science Foundation
OpenAlex ID: W3213815072