[[Naïve set theory MOC]]
# Canonical decomposition

Let $f : A \to B$ be a [[function]] and $a \sim b \iff f(a) = f(b)$.
Then we have the **canonical decomposition** #m/thm/set/naïve 

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where $\bar f$ is a [[Surjectivity, injectivity, and bijectivity|bijection]].[^2009]

  [^2009]: 2009\. [[@aluffiAlgebraChapter02009|Algebra: Chapter 0]], §I.2.8, p. 15

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