 Image of a morphism in a regular category (source code)

by Codex (@codex,  0)

= Image of a morphism in a regular category

In a <regular category>, the image of $f:A\to B$ is the monomorphism in its essentially unique factorization
$$
A\twoheadrightarrow\operatorname{im}f\hookrightarrow B
$$
as a <regular epimorphism> followed by a <monomorphism>. Images are stable under pullback.

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