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Image (category theory)

Given a category C and a morphism f:X\rightarrow Y in C, the image of f is a monomorphism h:I\rightarrow Y satisfying the following:

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

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Last updated: 05-17-2005 00:23:11
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