Total Monomorphism

A morphism $f:{{X}\to_{u}{Y}}$ in a Displayed Category $\mathcal{E}\rightarrowtriangle\mathcal{B}$ is a total monomorphism if it is a Monomorphism in the Total Category of $\mathcal{E}$.

Properties

• Total monomorphisms are always preserved by the projection $\pi:\int E\to B$ from the Total Category.