Cocartesian Morphism

A morphism $f:{{X}\to_{u}{Y}}$ over $u:{{A}\to{B}}$ in a Displayed Category $\mathcal{E}\rightarrowtriangle\mathcal{B}$ is cocartesian if

• For all $v:{{B}\to{C}}$ and $h:{{X}\to_{v\circ u}{Z}}$, there exists a unique $[v,h]$ such that $[v,h]\circ f=h$.

Properties

• A morphism is cocartesian if and only if it is Cartesian in the Total Opposite of $\mathcal{E}$.