Theorems · Theorem · category theory

CategoryTheory.PreGaloisCategory.comp_autMap

∀ {C : Type u₁} [inst : CategoryTheory.Category.{u₂, u₁} C] [inst_1 : CategoryTheory.GaloisCategory C] {A B : C}
  [inst_2 : CategoryTheory.PreGaloisCategory.IsConnected A] [inst_3 : CategoryTheory.PreGaloisCategory.IsGalois B]
  (f : A ⟶ B) (σ : CategoryTheory.Aut A),
  CategoryTheory.CategoryStruct.comp f (CategoryTheory.PreGaloisCategory.autMap f σ).hom =
    CategoryTheory.CategoryStruct.comp σ.hom f

Defined in

Mathlib.CategoryTheory.Galois.GaloisObjects

Cited by

2 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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