Tensor product $H$ -module

Let $H$ be a Hopf $K$ -algebra and $𝑅, 𝐵$ be $H$ -modules. Then the $K$ -tensor product $𝑅 \otimes K 𝐵$ of the underlying $K$ -modules has a canonical $H$ -module structure via the action #m/def/hopf

𝑥 (𝑣 \otimes 𝑤) = \sum (𝑥) 𝑥 (1) 𝑣 \otimes 𝑥 (2) 𝑤

or string diagramatically

#state/tidy | #lang/en | #SemBr

Tensor product H-module

Tensor product $H$ -module