Yeah, that's correct. You also often see it as having that for any method `X -> T<Y>` there's a corresponding method `T<X> -> T<Y>`. Or you can have that for any two arrows `X -> T<Y>` and `Y -> T<Z>` there's a composed arrow `X -> T<Z>`. All are equivalent.
Thanks for confirming; I wasn’t 100% sure what I wrote was equivalent to the `X -> T<Y>` definition, but I could see how you’d get one from the other using the unit/counit.
