Theorems · Theorem · category theory

CategoryTheory.NatIso.isIso_of_isIso_app

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F G : CategoryTheory.Functor C D} (α : F ⟶ G) [∀ (X : C), CategoryTheory.IsIso (α.app X)], CategoryTheory.IsIso α

A natural transformation is an isomorphism if all its components are isomorphisms.

Defined in

Mathlib.CategoryTheory.NatIso

Cited by

11 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsIso