comonad
A comonad is a concept from category theory that is dual to a monad. Formally, it consists of a functor W: C → C together with two natural transformations: delta: W ⇒ W∘W (a comultiplication) and epsilon: W ⇒ Id (a counit). These must satisfy laws that are dual to the monad laws: coassociativity (delta followed by W(delta) equals delta followed by delta) and counit laws (epsilon after delta is the identity, and W(epsilon) after delta is also the identity). In essence, a comonad represents contexts that can be observed and duplicated.
In programming, comonads provide a way to model computations that are context-dependent and can be extended
- The Store comonad, parameterized by a set s. A value is represented as Store s a =
- The Environment (or pair) comonad, W a = (e, a) for a fixed environment e. extract (e,
Comonads arise in contexts such as dataflow modeling, context-aware computations, and structures like zippers or comonadic
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