> Why can I get from every Comonad an Monad, bu...

# arrow

[Imran/Malic]

Why can I get from every Comonad an Monad, but not the other way around?

[Imran/Malic]

essentially, I want to figure out when we have a Monad and a Comonad for free. Why can’t we get a Bimonad, too?

[simon.vergauwen]

Because they're not the same? I can extract the value from Id but not from Option, hence Id has a Comonad and Option doesn't.

[Imran/Malic]

makes sense, but are there any groups of categories where we can enforce this or at least derive that?

[simon.vergauwen]

Enforce what?

[Imran/Malic]

X is a Comonad -> there is a Monad -> thus there is a Bimonad

[raulraja]

Derivation will be nicer with compiler plugins but at the moment is better to specialize the implementations

[Miguel Coleto]

I think not every Comonad can give a Monad too

[Miguel Coleto]

For example the Day datatype cannot provide an instance for Monad

[Miguel Coleto]

But maybe I am wrong as I coded that datatype myself and couldn't see how to provide an implementation for flatMap

[Imran/Malic]

I am trying to understand this https://hackage.haskell.org/package/kan-extensions-5.2/docs/Control-Monad-Co.html
essentially Co introduces the later — to get a Monad from a Comonad. For me cat theory always takes time to digest 😅

[Miguel Coleto]

I left that datatype Todo after I could write an example using every datatype from arrow-ui and have a better understanding of Comonads