Example 2.2.5.1.4 (002Q): Examples of Coequalisers of Sets

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Here are some examples of coequalisers of sets.

Quotients by Equivalence Relations. Let $R$ be an equivalence relation on a set $X$. We have a bijection of sets
\[ X/\mathord {\sim }_{R}\cong \text{CoEq}\webleft (R\hookrightarrow X\times X\underset {\text{pr}_{2}}{\overset {\text{pr}_{1}}{\rightrightarrows }}X\webright ). \]

Proof of Example 2.2.5.1.4.

Item 1: Quotients by Equivalence Relations

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