## Epimorphisms are surjective

A morphism $h$ in a category is an ** epimorphism** if it is right-cancellative, i.e. for all
morphisms $f$, $g$ in the category $f\circ h=g\circ h$ implies $f=g$.

A function $h:A\to B$ is ** surjective** (or

**) if $B=f[A]=\{f(a): a\in A\}$, i.e., for all $b\in B$ there exists $a\in A$ such that $f(a)=b$.**

*onto*
** Epimorphisms are surjective** in a (concrete) category of structures if the underlying function of every epimorphism is surjective.

If a concrete category has the amalgamation property and all epimorphisms are surjective, then it has the strong amalgamation property^{1)}

^{1)}E. W. Kiss, L. Márki, P. Pröhle, W. Tholen,

**, Studia Sci. Math. Hungar.,**

*Categorical algebraic properties. A compendium on amalgamation, congruence extension, epimorphisms, residual smallness, and injectivity***18**, 1982, 79-140 MRreview

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