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Dima Pasechnik
Dima Pasechnik
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Take a Cartesian (or monoidal) closed category; define Reader monad for a given object E$E$ as X |-> X^E;$X \mapsto X^E$; and take a strong monad M $M$ (strong means preserves product or tensor product).

Now the composition M o E$M\circ E$ (M$M$ followed by E$E$) is a monad again.

At least I believe it is true; and I wonder if it is a known fact, or plain wrong.

Take a Cartesian (or monoidal) closed category; define Reader monad for a given object E as X |-> X^E; and take a strong monad M (strong means preserves product or tensor product).

Now the composition M o E (M followed by E) is a monad again.

At least I believe it is true; and I wonder if it is a known fact, or plain wrong.

Take a Cartesian (or monoidal) closed category; define Reader monad for a given object $E$ as $X \mapsto X^E$; and take a strong monad $M$ (strong means preserves product or tensor product).

Now the composition $M\circ E$ ($M$ followed by $E$) is a monad again.

At least I believe it is true; and I wonder if it is a known fact, or plain wrong.

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Vlad Patryshev
Vlad Patryshev
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Seems like Reader monad composed with a strong monad produces a monad, am I right?

Take a Cartesian (or monoidal) closed category; define Reader monad for a given object E as X |-> X^E; and take a strong monad M (strong means preserves product or tensor product).

Now the composition M o E (M followed by E) is a monad again.

At least I believe it is true; and I wonder if it is a known fact, or plain wrong.