2 problems

Let $G,G',H,H'$ be compact Lie monoids with morphisms $\varphi\colon G\to G'$ and $\psi\colon H\to H'$. Let $M,M'$ be nice enough symplectic manifolds acted on symplectically by…

Let $G,G',H,H'$ be compact Lie monoids, let $X,X'$ be closed smooth manifolds acted on by $G\times H$ and $G'\times H'$ respectively, let $\varphi\colon G\to G'$ and…