Proposal: lifting between monad transformers, simple effect types and raw types

In practice, I often encounter situations when I need to lift F[_] to EitherT or OptionT. For EitherT, the only current option is EitherT.right[E](foo: F[A]): EitherT[F, E, A]. Compare that to A-F[A] interop or OptionT-EitherT interop:

(a: A).pure[F]: F[A]
(o: OptionT[F, A]).toRight(error: E): EitherT[F, E, A]
(e: EitherT[F, E, A]).toOption: OptionT[F, A]

Similarly, I think it is a good idea to have rich wrappers such as to allow:

(fa: F[A]).toRight[E]: EitherT[F, E, A]
(fa: F[A]).toLeft[B]: EitherT[F, A, B]
(fe: F[Either[E, A]]).lift: EitherT[F, E, A]
(fo: F[Option[A]]).lift: OptionT[F, A]

The EitherT.right(foo: F[A]) is a bit cumbersome because:

• There's a redundancy of information: in general, right uniquely implies EitherT when used on F[A]
• You could solve the above redundancy by importing EitherT.{right, ...} – however, there is a bunch of conversion methods defined on EitherT, and the need to manage the imports might introduce some mental overhead. Ideally, I'd like to be able to just import Cats once (e.g. currently I am using import cats._, cats.implicits._, cats.data._, cats.effect._) and forget about it.
• There are extra parentheses: right[E](fa) vs fa.toRight. Parentheses clutter code.
• The syntax is not uniform with that of A: if I can do a.pure[EitherT[...]], I'd also like to be able to do fa.toRight[E].

Start by reading the existing EitherT.right entry point and the OptionT/EitherT conversion methods described in the proposal. Compare their syntax and semantics with the requested F[A].toRight, F[A].toLeft, and F[Either] or F[Option] lifting APIs; done requires an agreed scope and corresponding implementation and tests.