Diagonalization/ dupe for monads and tuples?

[Carter Schonwald]

It was pointed out to me in a private communication that the tuple function
\x->(x,x) is actually a special case of a diagonalization for biapplicative
and some related structures monadicially.  Another example in the same
flavor is pure impl for the applicative instance for sized lists.

diag x = bipure x x

So framed a litttle differently, there’s definitely an abstraction or
common pattern lurking here. Perhaps folks can help Tease this out. One
person I chatted with this morning alluded to it being relevant to
computational flavors of adjunctions or some such ? It def matters in a
different way when doing computation resource aware programming in a
symmetric monoidal category.

Let’s collect some ideas and patterns and get to the bottom of this!
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