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arXiv · 1704.00303

Homotopical algebra is not concrete

Fosco Loregian·Ivan Di Liberti
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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 $\text{ho}(\mathcal M)$ cannot be concrete. This result is part of an attempt to understand more deeply the relation between set theory and abstract homotopy theory.

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Fosco Loregian, Ivan Di Liberti. 2017-04-02. Homotopical algebra is not concrete. https://doi.org/10.1007/s40062-018-0197-3

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