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Monomorphism

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Definition

Definition with symbols

Suppose \mathcal{C} is a category, A,B \in \operatorname{Ob}\mathcal{C}, and f \in \mathcal{C}(A,B). We say that f is monic, or is a monomorphism, if for any object C and any g,h \in \mathcal{C}(C,A), we have:

f \circ g = f \circ h \implies g = h.

In other words, the morphism is left-cancellative.

Relation with other properties

Stronger properties

Related properties

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