= Nested partial unary operation category
{title2=$\mathcal C_n$}
An object of $\mathcal C_n$ is a set with a finite list of <partial unary operations>. The first is total; the domain of each later operation consists exactly of the defined <fixed points> of the immediately preceding operation. Morphisms preserve every defined operation. Take $\mathcal C_0$ to be the <Category of sets>. This tower gives examples of arbitrary finite <monadic length> even though its long free–forgetful composites induce the same first <monad>.
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