: Mathematics: monomorphism

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monomorphism

In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from $X$ to $Y$ is often denoted with the notation ${\\displaystyle X\\hookrightarrow Y}$ . In the more general setting of category theory, a monomorphism (also called a monic morphism or a mono) is a left-cancellative morphism. That is, an arrow $f : X \to Y$ such that for all objects $Z$ and all morphisms $g 1, g 2 : Z \to X$ ,
${\\displaystyle f\\circ g_{1}=f\\circ g_{2}\\implies g_{1}=g_{2}.}$

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