Definition 4.32.1. Let $\mathcal{C}$ be a category. Let $p : \mathcal{S} \to \mathcal{C}$ be a category over $\mathcal{C}$. A *strongly cartesian morphism*, or more precisely a *strongly $\mathcal{C}$-cartesian morphism* is a morphism $\varphi : y \to x$ of $\mathcal{S}$ such that for every $z \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{S})$ the map

given by $\psi \longmapsto (\varphi \circ \psi , p(\psi ))$ is bijective.

## Comments (1)

Comment #3991 by Praphulla Koushik on