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Thanks for all the additions.
Just to say that we also have writer comonad. I’ll add some cross-links. [edit: oh, you just did, it seems. Okay, great. ]
But looking at it now, that example “As a logging effect” (here) is not well construed: It advertises the interpretation of log messages but then never mentions free monoids and instead insists on writing the monoid operation additively and speaks of “adding up costs”.
This should be polished up further. But I’ll leave it as is for the time being.
added pointer to
for the writer monad in computer science
added pointer to:
(makes the construction of action monads an adjunction between monoids and strong monads)
and followups:
Martti Karvonen, Frobenius algebras in functor categories, Oxford (2014) [pdf, Karvonen-FrobeniusMonads.pdf:file]
Chris Heunen, Martti Karvonen, Monads on dagger categories, Theory and Applications of Categories 31 35 (2016) 1016-1043 [arXiv:1602.04324, tac:31-35]
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