The Equivalence Extension Property and Model Structures

2017/04/23 by Sattler, Christian · 1 citation
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1704.06911

Abstract

We give an elementary construction of a certain class of model structures. In particular, we rederive the Kan model structure on simplicial sets without the use of topological spaces, minimal complexes, or any concrete model of fibrant replacement such as Kan's Exⁱnfinity functor. Our argument makes crucial use of the glueing construction developed by Cohen et al. in the specific setting of certain cubical sets.

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