Hopf theory MOC

$H$ -hom module

Let $H$ be a Hopf $K$ -algebra and $𝑅, 𝐵$ be $H$ -modules. Then the $K$ -module

𝑅 ⊸ 𝐵 : = K 𝖬 𝗈 𝖽 (𝑅, 𝐵)

of $K$ -morphisms has a canonical $H$ -module structure via the action #m/def/hopf

(𝑥 𝑓) (𝑣) = \sum (𝑥) 𝑥 (1) 𝑓 (𝜎 (𝑥 (2)) 𝑣)

or in terms of string diagrams

Properties

$H$ -invariant $K$ -morphisms are $H$ -morphisms

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