The cube axiom and resolutions in homotopy theory

2021/10/18 by Stelzer, Manfred
#55Q05 #55Q20 #55U35 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.09119

Abstract

We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model structure. As an application, classical theorems in unstable homotopy theory are extended to this context.

Related

• The realization space of an unstable coalgebra
• The diagonal of cellular spaces and effective algebro-homotopical constructions
• Alternate proofs for the n-dimensional resolution theorems
• Stability conditions and crepant small resolutions
• The homotopy automorphisms of a marked n-stage