Editing Monad (category theory) (section)

====The environment monad====

{{Expand section|date=February 2023|with=describe multiplication}}

Given a set <math>E</math>, the endofunctor of the '''reader''' or '''environment monad''' maps each set <math>X</math> to the set of functions <math>E\to X</math>. Thus, the endofunctor of this monad is exactly the [[hom functor]] <math>\mathrm{Hom}(E, -)</math>. The component of the unit at <math>X</math> maps each element <math>x\in X</math> to the [[constant function]] <math>e\mapsto x</math>.

In functional programming and denotational semantics, the environment monad models computations with access to some read-only data.