 If "X" is an object of "C", an "equivalence relation" "R" on "X" is a map "R" → "X" × "X" in "C"
such that for any object "Y" in "C", the induced map Hom("Y", "R") → Hom("Y", "X") × Hom("Y", "X") gives an ordinary equivalence relation on the set Hom("Y", "X").Since "C" has colimits we may form the coequalizer of the two maps "R" → "X"; call this "X"/"R".The equivalence relation is "effective" if the canonical map

is an isomorphism.