Definition:Monomorphism (Category Theory)
Let $\mathbf C$ be a metacategory.
A monomorphism is a morphism $f \in \mathbf C_1$ such that:
- $f \circ g = f \circ h \implies g = h$
One writes $f: C \rightarrowtail D$ to denote that $f$ is a monomorphism.
Also known as
Often, monomorphism is abbreviated to mono.
Alternatively, one can speak about a monic morphism to denote a monomorphism.
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.