If you want to know more how Kleisli morphisms are used in Я I recommend you to check out Bind and traverse with Kleisli morphisms article.
Kleisli morphisms in Я look like this:
into a (t o)
Just like for Hom Functors, in Я Kleisli morphism just named after shape of Kleisli categories - Functor in this morpshism doesn’t have to be a Monad.
This type of arrows often used for binding effects and traversing structures with these operators: