[[!include 2-category theory - contents]]
[[!include higher algebra - contents]]
Formally dually to how a monad has a Kleisli category so also a comonad $P \colon \mathcal{C}\to\mathcal{C}$ has a (co-)Kleisli category: its objects are the objects of $\mathcal{C}$, a morphism $f \colon c_1 \to c_2$ in the co-Kleisli category is a morphism
in $\mathcal{C}$, and the composition of two such in the co-Kleisli category is represented by the morphism in $\mathcal{C}$ given by
For an idempotent comonad the co-Kleisli category is the coreflective subcategory of its modal types.
For $P= Jet$ a jet comonad, then morphisms in its coKleisli category are differential operators.
The Kleisli category of a comonad can be used to model call-by-name? programming languages.
Last revised on September 22, 2017 at 16:10:02. See the history of this page for a list of all contributions to it.