Theorems · Theorem · category theory

CategoryTheory.PreGaloisCategory.exists_autMap

∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] [inst_1 : CategoryTheory.GaloisCategory C] {A B : C}
  (f : A ⟶ B) [CategoryTheory.PreGaloisCategory.IsConnected A] [CategoryTheory.PreGaloisCategory.IsGalois B]
  (σ : CategoryTheory.Aut A),
  ∃! τ, CategoryTheory.CategoryStruct.comp f τ.hom = CategoryTheory.CategoryStruct.comp σ.hom f

For a morphism from a connected object A to a Galois object B and an automorphism of A, there exists a unique automorphism of B making the canonical diagram commute.

Defined in

Mathlib.CategoryTheory.Galois.GaloisObjects

Cited by

2 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.GaloisCategoryCategoryTheory.PreGaloisCategory.IsConnectedCategoryTheory.PreGaloisCategory.IsGalois