Identifying the name of a theorem

[nuuskur]

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:
\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}

 

[Stephen Tashi]

As I interpret your symbols, the theorem is: http://en.wikipedia.org/wiki/Fundamental_theorem_on_homomorphisms.

This theorem and related theorems are presented as "commutative diagrams".