Image (Category Theory)

1. There exists a morphism $g:X\backslash rightarrow\; I$ such that f = hg.
2. For any object Z with a morphism $k:X\backslash rightarrow\; Z$ and a monomorphism $l:Z\backslash rightarrow\; Y$ such that f = lk, there exists a unique morphism $m:I\backslash rightarrow\; Z$ such that k = mg and h = lm.

• universal property
• subobject
• coimage
• image (mathematics)

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