A monad is defined as a monoid in the category of endofunctors: it encapsulates a value and provides a mechanism (bind) for applying a computation to that value while returning a result of the same structural shape (an endofunctor), and it satisfies monoid laws of associativity and identity via a unit operation. This structure guarantees that sequential composition of monadic operations is equivalent to direct function application, which allows side effects and control-flow branching (such as absence of a value) to be encapsulated within the monad rather than handled by external control logic. The concept belongs to category theory as applied to functional programming, building on the more general notions of functor and endofunctor, and underlies patterns such as railway-oriented programming as an alternative to exception-based error handling.
A monad is defined as a monoid in the category of endofunctors: it encapsulates a value and provides a mechanism (bind) for applying a computation to that value while returning a result of the same s…