Every adjunction gives rise to a comonad.
Adjunctions compose in a natural fashion.
Adjunctions compose in a natural fashion. If F -| G
is an adjunction, and P -| Q
is an
adjunction, then PF -| GQ is an adjunction. In fact, adjunctions in Scala form a monoid.
Extracts a value out of the comonad.
Every F
-algebra maps to a G
-coalgebra.
Every adjunction gives rise to a monad.
Every adjunction is representable.
Every G
-coalgebra maps to an F
-algebra.
Puts a value into the monad.
Adjoint functors annihilate each other.
Adjoint functors annihilate each other.
An adjunction formed by two functors
F
andG
such thatF
is left-adjoint toG
. The composite functor GF is a monad and the composite functor FG is a comonad.The minimal definition is either (unit, counit) or (leftAdjunct, rightAdjunct)