Theorems · Definition · category theory

CategoryTheory.isoCartesianComon

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      (A : CategoryTheory.Comon C) → A ≅ (CategoryTheory.cartesianComon C).obj A.X

Every comonoid object in a Cartesian monoidal category is equivalent to the canonical comonoid structure on the underlying object.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Comon_

Cited by

3 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory