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== Other properties ==
{{See also|List of set identities and relations#Functions and sets}}
[[Image:Injective composition2.svg|thumb|300px|The composition of two injective functions is injective.]] * If <math>f</math> and <math>g</math> are both injective then <math>f \circ g</math> is injective.
* If <math>g \circ f</math> is injective, then <math>f</math> is injective (but <math>g</math> need not be).
* <math>f : X \to Y</math> is injective if and only if, given any functions <math>g,</math> <math>h : W \to X</math> whenever <math>f \circ g = f \circ h,</math> then <math>g = h.</math> In other words, injective functions are precisely the [[monomorphism]]s in the [[category theory|category]] '''[[Category of sets|Set]]''' of sets.
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