Definition 4.33.1. 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
\[ \mathop{\mathrm{Mor}}\nolimits _\mathcal {S}(z, y) \longrightarrow \mathop{\mathrm{Mor}}\nolimits _\mathcal {S}(z, x) \times _{\mathop{\mathrm{Mor}}\nolimits _\mathcal {C}(p(z), p(x))} \mathop{\mathrm{Mor}}\nolimits _\mathcal {C}(p(z), p(y)), \]
given by $\psi \longmapsto (\varphi \circ \psi , p(\psi ))$ is bijective.
Comments (1)
Comment #3991 by Praphulla Koushik on