论文标题
在Hofmann-Streicher宇宙上
On Hofmann-Streicher universes
论文作者
论文摘要
我们又一看了霍夫曼（Hofmann）的构建和宇宙$（u，{\ mathsf {e} l}）$的解释，以解释Martin-Löf类型理论在Presheaf类别$ \ psh {\ c} $中。事实证明，分类器$ \ dot {\ dot {\ dot {\ set}^{\ mathsf {op}} \ to in Is Isvibration in Is Is Incriptation in Si y IS IS IS IS IS SOIRET，$（u，{u，{u，{u，{u，{u，{u，{u，{u，{u，{u，{u，{u，{u，{u，{u，{u，{u，{u，{\ r，{\ r，{\ o，{\ r，{\ r，{\ nersf {e} l}）$ ````grothendieck construction''取前$ p：\ op {\ c} \ to \ set $ set $ to其元素类别$ \ int_ \ c p $。我们还考虑了此类宇宙以及结构化家族的宇宙（例如纤维化）的基础变化。
We have another look at the construction by Hofmann and Streicher of a universe $(U,{\mathsf{E}l})$ for the interpretation of Martin-Löf type theory in a presheaf category $\psh{\C}$. It turns out that $(U,{\mathsf{E}l})$ can be described as the \emph{categorical nerve} of the classifier $\dot{\Set}^{\mathsf{op}} \to \op{\Set}$ for discrete fibrations in $\Cat$, where the nerve functor is right adjoint to the so-called ``Grothendieck construction'' taking a presheaf $P : \op{\C}\to\Set$ to its category of elements $\int_\C P$. We also consider change of base for such universes, as well as universes of structured families, such as fibrations.
