Editing Monad (category theory) (section)

====The maybe monad====

The endofunctor of the '''maybe''' or '''partiality''' monad adds a disjoint point:{{sfn|Riehl|2017|p=155}}

:<math>(-)_{*}: \mathbf{Set}\to\mathbf{Set}</math>
:<math>X\mapsto X\cup\{*\}</math>

The unit is given by the inclusion of a set <math>X</math> into <math>X_*</math>:

:<math>\eta_X: X\to X_{*}</math>
:<math>x\mapsto x</math>

The multiplication maps elements of <math>X</math> to themselves, and the two disjoint points in <math>(X_{*})_{*}</math> to the one in <math>X_{*}</math>.

In both functional programming and denotational semantics, the maybe monad models [[Partial function|partial computations]], that is, computations that may fail.