a design pattern

In functional programming, a monad is a design pattern that allows structuring programs generically while automating away boilerplate code needed by the program logic.

a monoid in the category of endofunctors

“A monad is just a monoid in the category of endofunctors”.

a Monoid

Probably should, though a monad is a monoid so a monad all works out.

that wraps another object

A monad is an object that wraps another object.

a structure that represents computations

In programming, a monad is a structure that represents computations.

an endofunctor () a functor mapping a category to itself

In category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is an endofunctor (a functor mapping a category to itself), together with two natural transformations required to fulfill certain coherence conditions.

a functor you can flatten

*: 'A monad is a functor you can flatten.

an algebraic structure in category theory

A monad is an algebraic structure in category theory, and in Haskell it is used to describe computations as sequences of steps, and to handle side effects such as state and IO.

a functor together with some natural transformations

Recall that a monad is a functor together with some natural transformations

a simple kind of error monad, where all errors are represented by Nothing

a monad is a simple kind of error monad, where all errors are represented by Nothing.

a container type

*: 'A monad is a container type together with a few methods defined on a few methods .

a triple of a type

For our purposes, a monad is a triple of a type and '''then''' & '''return''' operators defined over a type so that the following laws apply: ...' *: 'For our purposes, a monad is a triple of a type and ''then>'' & ''return'' operators defined over a type so that the following laws apply: ...' *: Written when 'what is a monad' started becoming an FAQ.

an abstraction

A monad is just an abstraction, albeit a useful one.

an applicative functor that lets you transition a value to a new context within the same type hierarchy

A monad is an applicative functor that lets you transition a value to a new context within the same type hierarchy.

a special kind of a functor

A monad is a special kind of a functor.

a structure that defines a way to combine functions

A monad is a structure that defines a way to combine functions.

a functor M equipped with two additional polymorphic functions

A monad is a functor M equipped with two additional polymorphic functions; One from A to M[A] and one from M[M[A]] to M[A].

a functor which attaches 'context' to a value, which has a way to inject a value into the monad, and which has a way to evaluate values with respect to the context attached to a way , at least in a restricted way

The long story is that a monad is a functor which attaches 'context' to a value, which has a way to inject a value into the monad, and which has a way to evaluate values with respect to the context attached to a way , at least in a restricted way.

a functor MM (on some category CC

Analogously, a monad is a functor MM (on some category CC, so a functor M:C→CM: C \to C) that is equipped with a “multiplication” mm which is a natural transformation m:MM→Mm: M M \to M, and a “unit” ee, which is a natural transformation e:1 C→Me:

an 'independent' spiritual or divine entity

Strictly speaking, a monad is an 'independent' spiritual or divine entity in continuous evolution on continuous evolution's own plane; in other words, a relatively full-blown god.