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

Let $H$ be a Hopf $K$ -algebra and $𝑅, 𝐵$ be $H$ -modules. Then the space of $H$ -invariants $(𝑅 ⊸ 𝐵) H$ in the $H$ -hom module is precisely the space of $H$ -morphisms. #m/thm/hopf

Proof

If $𝑓 : 𝑅 \to 𝐵$ is an $H$ -morphism, then

so $𝑓 \in (𝑅 ⊸ 𝐵) H$ . Conversely, if $𝑓 \in (𝑅 ⊸ 𝐵) H$ then

so $𝑓$ is an $H$ -morphism.

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

H-invariant K-morphisms are H-morphisms