Return to Revisions

If $A\times (-)$ is a left adjoint, it must commute with colimits, and in particular, $\oplus$.

That is, write $B_1\oplus B_2$ as $colim_i B_i$, then $A\times colim_iB_i\cong colim_i(A\times B_i)$, from which the result follows.