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arxiv: 1111.3489 · v1 · pith:7ZUV4UTYnew · submitted 2011-11-15 · 🧮 math.CT

The univalence axiom in posetal model categories

classification 🧮 math.CT
keywords axiommodelunivalencecategoriesposetalabstractalbeitasking
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In this note we interpret Voevodsky's Univalence Axiom in the language of (abstract) model categories. We then show that any posetal locally Cartesian closed model category $Qt$ in which the mapping $Hom^{(w)}(Z\times B,C):Qt\longrightarrow Sets$ is functorial in $Z$ and represented in $Qt$ satisfies our homotopy version of the Univalence Axiom, albeit in a rather trivial way. This work was motivated by a question reported in [Ob], asking for a model of the Univalence Axiom not equivalent to the standard one.

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