Kleisli category

A Kleisli - category is a category which arises naturally from a monad. It is named after the Swiss mathematician Heinrich Kleisli.

Definition

Be a category and a monad, with as Endofunktor and, as laid down at him monoid operations. To and associated Kleisli category is referred to as. The objects and morphisms in it are

  • , and
  • .

Identitätsmorphismen and concatenation are

  • And
  • .

Examples

  • Correspondences form a Kleisli category. The Endofunktor on set is here powerset education, with.
Monad (category theory)
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