## 1. Representability of fibrations Let $X$ be a simplicial set, let . $W_\alpha(X)$ denote the class of well ordered morphisms $f:Y\to X$. Then the assignation $X\mapsto W_\alpha_X$ is a functor which is representable by the functor $y^{op}\circ y^{op}:\Delta^{op}\to Set$ where $y$ is Yoneda (...) ## References * Kapulkin, Lumsdaine, Voevodsky, univalence in simplicial sets For a different model of the univalence axiom: * Ieke Moerdijk, Fiber Bundles and Univalence For universes: * [[nLab:Thomas Streicher]], _Universes in Toposes_, In: _From sets and types to topology and analysis: towards practicable foundations for constructive mathematics_ ([ps](http://www.mathematik.tu-darmstadt.de/~streicher/NOTES/UniTop.ps.gz),[pdf](http://www.mathematik.tu-darmstadt.de/~streicher/NOTES/UniTop.pdf)) For references and recent contributions on cordials: * Joan Bagaria, [[Carles Casacuberta]], Adrian Mathias, [[Jiri Rosicky]] _Definable orthogonality classes in accessible categories are small_, [arXiv](http://arxiv.org/abs/1101.2792) {#BagariaCasacubertaMathiasRosicky}