Definition. A natural model ([Awodey 2016Awodey, S. 2016. Natural models of homotopy type theory. Mathematical Structures in Computer Science 28, 241–286. http://dx.doi.org/10.1017/S0960129516000268.]) consists of a category $\mathsf{C}$ along with presheaves $\mathsf{Ty},\mathsf{Tm}:{\mathsf{C}}^{\mathrm{op}}\to \mathsf{Set}$ and a representable natural transformation $u:\mathsf{Tm}\to \mathsf{Ty}$. This means that for any $\Gamma \in \mathsf{C}$, $A\in \mathsf{Ty}(\Gamma )$, there exists a pullback square