Theorems · Theorem · category theory

CategoryTheory.Comonad.coalgebra_iso_of_iso

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (G : CategoryTheory.Comonad C) {A B : G.Coalgebra}
  (f : A ⟶ B) [CategoryTheory.IsIso f.f], CategoryTheory.IsIso f

Given a coalgebra morphism whose carrier part is an isomorphism, we get a coalgebra isomorphism.

Defined in

Mathlib.CategoryTheory.Monad.Algebra

Cited by

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Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsIso