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The Kleisli category of a Monad $T$ on $\mathcal{C}$, denoted $Kl T$ or $\mathcal{C}_T$, is the category:

• Objects are the objects of $\mathcal{C}$
• Morphisms are $\mathcal{C}_T(A,B) := \mathcal{C}(A,TB)$
• Composition.
• Identity