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Homotopical algebra is not concrete

2017/04/02 by Loregian, Fosco, Di Liberti, Ivan
#18A22 #18E35 #18G55 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1704.00303

Abstract

We generalize Freyd's well-known result that "homotopy is not concrete", offering a general method to show that under certain assumptions on a model category \mathcal M, its homotopy category ho(\mathcal M) cannot be concrete. This result is part of an attempt to understand more deeply the relation between set theory and abstract homotopy theory.

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