Commutative Strong Monads
For every strong monad T on a symmetric monoidal category, a costrength natural transformation can be defined by
- .
A strong monad T is said to be commutative when the diagram
commutes for all objects and .
One interesting fact about commutative strong monads is that they are "the same as" symmetric monoidal monads. More explicitly,
- a commutative strong monad defines a symmetric monoidal monad by
- and conversely a symmetric monoidal monad defines a commutative strong monad by
and the conversion between one and the other presentation is bijective.
Read more about this topic: Strong Monad
Famous quotes containing the word strong:
“It is funny that men who are supposed to be scientific cannot get themselves to realise the basic principle of physics, that action and reaction are equal and opposite, that when you persecute people you always rouse them to be strong and stronger.”
—Gertrude Stein (1874–1946)