Homotopical algebra is not concrete

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 \(\text{ho}(\mathcal M)\) cannot be concrete. This result is part of an attempt to unders...

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Bibliographic Details
Published inarXiv.org
Main Authors Loregian, Fosco, Ivan Di Liberti
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 26.01.2018
Subjects
Homotopy theory
Mathematics - Algebraic Topology
Mathematics - Category Theory
Mathematics - Logic
Set theory
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Summary: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 \(\text{ho}(\mathcal M)\) cannot be concrete. This result is part of an attempt to understand more deeply the relation between set theory and abstract homotopy theory.
ISSN:2331-8422
DOI:10.48550/arxiv.1704.00303