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~ such that for every ''x'' ∈ ''X'', we have ''f''(''x'') ~ ''g''(''x''). In particular, if R is an equivalence relation on a set Y, and r₁, r₂ are the natural projections (''R'' ? ''Y'' × ''Y'') -> ''Y'' then the coequalizer of r₁ and r₂ is the quotient set ''Y'' / ''R''. (See also: quotient by an equivalence relation.)
* The coequalizer in the category of groups is very similar.

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