Definition:Epimorphism (Abstract Algebra)

Definition
A homomorphism which is a surjection is described as epic, or called an epimorphism.

Category Theory
In a category $\mathcal C$, an epimorphism is a morphism $\alpha \in \operatorname{mor}\mathcal C$ such that $\beta\alpha = \gamma \alpha$ implies $\beta = \gamma$ for all morphisms $\beta,\gamma \in \operatorname{mor}\mathcal C$ for which the composition is defined.

Linguistic Note
The word epimorphism comes from the Greek morphe (μορφή) meaning form or structure, with the prefix epi- meaning onto.

Thus epimorphism means onto (similar) structure.