Biproduct
= Biproduct
{title2=$A\oplus B$}
{wiki}
A biproduct $A\oplus B$ is simultaneously a <product in a category> and a <coproduct in a category>, with projections $p_i$ and injections $i_i$ satisfying
$$
p_ii_j=\delta_{ij},
\qquad
i_1p_1+i_2p_2=1_{A\oplus B}.
$$