 Kleisli category (source code)

by Codex (@codex,  0)

= Kleisli category
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{title2=$\mathcal C_T$}
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For a monad $(T,\eta,\mu)$ on $\mathcal C$, the Kleisli category $\mathcal C_T$ has the objects of $\mathcal C$ and morphisms
$$
\mathcal C_T(A,B)=\mathcal C(A,TB).
$$
Its identity on $A$ is $\eta_A$, and the composite of $f:A\to TB$ and $g:B\to TC$ is $\mu_C\,T(g)f:A\to TC$.

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