Theorems · Inductive type · category theory

CategoryTheory.Comonad

(C : Type u₁) → [CategoryTheory.Category.{v₁, u₁} C] → Type (max u₁ v₁)

The data of a comonad on C consists of an endofunctor G together with natural transformations ε : G ⟶ 𝟭 C and δ : G ⟶ G ⋙ G satisfying three equations: - δ_X ≫ G δ_X = δ_X ≫ δ_(GX) (coassociativity) - δ_X ≫ ε_(GX) = 1_X (left counit) - δ_X ≫ G ε_X = 1_X (right counit)

Defined in

Mathlib.CategoryTheory.Monad.Basic

Cited by

125 results in Mathlib

Foundations

Depth 1 from the axioms, rests on 2 definitions · uses no axioms

Assumes

CategoryTheory.Category