Internal and local homotopy theory

Zhen Lin Low

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arXiv · 1404.7788

Internal and local homotopy theory

Zhen Lin Low

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Abstract

There is a well-established homotopy theory of simplicial objects in a Grothendieck topos, and folklore says that the weak equivalences are axiomatisable in the geometric fragment of $L_{\omega_1, \omega}$. We show that it is in fact a theory of presheaf type, i.e. classified by a presheaf topos. As a corollary, we obtain a new proof of the fact that the local Kan fibrations of simplicial presheaves that are local weak homotopy equivalences are precisely the morphisms with the expected local lifting property.

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BibTeX RIS

Zhen Lin Low. 2014-04-30. Internal and local homotopy theory. https://arxiv.org/abs/1404.7788

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