Explaining monad transformers in categorical terms Most resource regarding categorical notions in programming describe monads, but I've never seen a categorical description of monad transformers.

How could monad transformers be described in the terms of category theory?

In particular, I'd be interested in:


the relationship between monad transformers and their corresponding base monads;
the relationship between them and the monads they're transforming into new monads;
monad transformer stacks.
According to Oleksandr Manzuk, they are "translation of a monad along an adjunction", see "Calculating Monad Transformers with Category Theory". By the way, that's the third hit on Google for "monad transformer categorically". The first is a Stackoverflow question about this and the second is your question.