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
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