We present Voevodsky’s construction of a model of univalent type theory in the category of simplicial sets.

To this end, we first give a general technique for constructing categorical models of dependent type theory, using universes to obtain coherence. We then construct a (weakly) universal Kan fibration, and use it to exhibit a model in simplicial sets. Lastly, we introduce the Univalence Axiom, in several equivalent formulations, and show that it holds in our model.

As a corollary, we conclude that Martin-Löf type theory with one univalent universe (formulated in terms of contextual categories) is at least as consistent as ZFC with two inaccessible cardinals.

中文翻译：

---

单价基础的简单模型（在Voevodsky之后）

我们在简单集类别中介绍Voevodsky的单价类型理论模型的构造。

为此，我们首先给出一种通用技术，用于构造依赖类型理论的分类模型，并使用宇宙获得连贯性。然后，我们构造一个（弱）通用Kan纤维，并使用它在简单集中展示一个模型。最后，我们以几种等效的方式介绍Univalence公理，并证明它在我们的模型中成立。

作为推论，我们得出结论，具有一个单价宇宙（根据上下文类别来表示）的Martin-Löf类型理论至少与具有两个不可访问的基数的ZFC一致。