**Background:** In homological algebra, a *quasi-isomorphism* of chain complexes is a chain map$\phi:(C,d) \to (C',d')$ so that the induced map on homology $\phi_\ast:H_\ast(C,d) \to H_\ast(C',d')$ is an isomorphism.

This is clearly a special instance of the following much more general phenomenon: given a functor $\mathcal{F}:\mathcal{C} \to \mathcal{D}$, between categories $\mathcal{C}$ and $\mathcal{D}$, a morphism in $\mathcal{C}$ is taken to an isomorphism in $\mathcal{D}$ by $\mathcal{F}$.

What is the standard terminology for a morphism of $\mathcal{C}$ so that its image under $\mathcal{F}$ is a (mono, epi, iso) morphism?

I couldn't find a term for this in MacLane's book, but I'm sorry if this is standard stuff.