Identifying the name of a theorem

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English is not my first language, all the material I have is in Estonian/Russian. The direct translation of it is something like:
Theorem on canonical factorization of functions - however googling it yields no meaningful result, therefore I'm guessing I have something wrong in the English terminology (I would like to know its English name). The theorem statement in mathematical terms goes as follows:
[itex]\forall f\colon X\to Y, \exists g\colon X/ \ker{f}\to Y\ \ | f = g\cdot\kappa\colon\ \ \kappa\colon X\to X/ \ker{f}[/itex]
 
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