  We study the positions in the Weihrauch lattice of parallel products of
various combinatorial principles related to Ramsey's theorem. Among other
results, we obtain an answer to a question of Brattka, by showing that Ramsey's
theorem for pairs ($\mathsf{RT}^2_2$) is strictly Weihrauch below the parallel
product of the stable Ramsey's theorem for pairs and the cohesive principle
($\mathsf{SRT}^2_2 \times \mathsf{COH}$).
