Menu
I'm just wondering whether there's a concise term for something that's both a monad and a comonad. I've done some searching, and I know these structures exist, but I haven't found a name for them.
201
Comonad is a Functor and provides duals of the Monad pure and flatMap functions. A dual to a function has the same types but the direction of the arrows are reversed. Whether or not that is useful, or even possible, depends on the particular type.
A monad is a structure that is a lot like a monoid, but that lives in a bicategory rather than a monoidal category. In other words, the concept of a monad is a vertical categorification of that of a monoid. Monads are among the most pervasive structures in category theory and its applications.
Such a creature, subject to certain conditions, is sometimes called a "Hopf monad" or a "Bimonad" (http://ncatlab.org/nlab/show/Hopf+monad).
However, this also requires fulfilling a number of axioms regarding distributive properties, and I haven't seen it come up in a programming context in any particular way.
154
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With
