Pushout in a category
= Pushout in a category
{title2=$B\amalg_A C$}
A pushout of $B\leftarrow A\to C$ is a <colimit> with morphisms $B\to P$ and $C\to P$ making the square commute and universal among such commuting pairs. In the <Category of sets>, form the disjoint union of $B,C$ and identify the two images of each element of $A$.