We also have



diag = join bipure



and (in pseudo-Haskell)



diag = unJoin . pure

  where

    newtype Join f a = Join { unJoin :: f a a } deriving (Functor)

    deriving instance Biapplicative f => Applicative (Join f)



The latter seems on its face potentially related to the instance for

lists of fixed length, but i am not sure how deep the connection may

be.