Coequalizer of a reflexive pair from a pushout
= Coequalizer of a reflexive pair from a pushout
For a <reflexive pair> $f,g:A\rightrightarrows B$ with common section $r$, form the <pushout in a category> of $f$ and $g$, with maps $j_1,j_2:B\to P$. The equation $j_1f=j_2g$, composed with $r$, gives $j_1=j_2=q$. This common map is a <coequalizer> of $f,g$: every map equalizing them defines a commuting pair into the pushout and hence factors uniquely through $q$.