Monad Transformer Lenses

I'll talk a bit about how we can do lenses in much more general settings. Then, given that the venue is "Monadic Warsaw" I'll show how we can build a monoidal category of monad transformers and work with lenses on this category with an eye towards how this can let us produce much more efficient code than we can with just the MTL classes as we know them today.
No real prior exposure to lenses is required, and all talk of profunctors and the like should be self-contained, but some basic understanding of monad transformers would be helpful.