Kleisli Category

Given a monad $(T,\eta ,\mu )$ on $\mathcal{C}$:

• Objects: same as $\mathcal{C}$
• Morphisms: $A{\to }_{T}B\equiv A\to T(B)$
• Identity: ${\eta }_A:A\to T(A)$
• Composition: $f^{♯}:A\to T(B),g^{♯}:B\to T(C)\Rightarrow {\mu }_C\circ T(g^{♯})\circ f^{♯}$

Defines category ${\mathcal{C}}_T$