Comonad

A comonad is a triple $(G,\epsilon ,\delta )$ where:

• $G:\mathcal{C}\to \mathcal{C}$ is an endofunctor
• $\epsilon :G\Rightarrow {\text{Id}}_{\mathcal{C}}$ (counit)
• $\delta :G\Rightarrow G^2$ (comultiplication)

Satisfying:

1. Coassociativity: $\delta \circ \delta =G\delta \circ \delta$
2. Counit: $G\epsilon \circ \delta ={\text{id}}_G={\epsilon }_G\circ \delta$