Definition:Monomorphism (Category Theory)

Definition
Let $\mathcal C$ be a category.

A monomorphism is a morphism $\alpha \in \operatorname{mor}\mathcal C$ such that:
 * $\alpha\beta = \alpha\gamma \implies \beta = \gamma$

for all morphisms $\beta, \gamma \in \operatorname{mor}\mathcal C$ for which the composition is defined.

Linguistic Note
The word monomorphism comes from the Greek morphe (μορφή) meaning form or structure, with the prefix mono- meaning single.

Thus monomorphism means single (similar) structure.