Definition:Epimorphism (Category Theory)

Definition
Let $\mathcal C$ be a category.

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.