Monad

A monad is a monoid in the bicategory of categories.

See also.

• extension system, or monad in relative form.
• distributive law
  • String diagrams for monad and monad algebras
• Centre of a monad in Set
• Strong monad
  • Do notation for strong monads
  • strong extension system
  • Effects of a monad
• monoidal monad, copy and discard monad, Frobenius monad
• algebra for a monad
• concurrent monad

Examples. Examples of monads include the continuation monad, the list monad, the distribution monad, or the state monad. Let us list here some examples of Set-based monads.

• maybe monad
• list monad (or free monoid monad).
• state monad, writer monad, update monad, reader monad.
• powerset monad, non-empty powerset monad
• distribution monad (and Giry monad), expectation monad, partial distribution monad.
• continuation monad