File:Strong monad commutation.png

Coherence law for commutative strong monads.

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\[
\xymatrix{
  &T(TA\otimes B)\ar[r]^{T(t'_{A,B})}&T^2(A\otimes B)\ar[dr]^{\mu_{A\otimes B}}\\
  TA\otimes TB\ar[ur]^{t_{TA,B}}\ar[dr]_{t'_{A,TB}}&&&T(A\otimes B)\\
  &T(A\otimes TB)\ar[r]_{T(t_{A,B})}&T^2(A\otimes B)\ar[ur]_{\mu_{A\otimes B}}
}
\]
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