Theorems · Definition · category theory

CategoryTheory.PreGaloisCategory.fiberBinaryProductEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{u₂, u₁} C] →
    (F : CategoryTheory.Functor C FintypeCat) →
      [inst_1 : CategoryTheory.PreGaloisCategory C] →
        [CategoryTheory.PreGaloisCategory.FiberFunctor F] →
          (X Y : C) → (F.obj (X ⨯ Y)).obj ≃ (F.obj X).obj × (F.obj Y).obj

The fiber of the binary product is the binary product of the fibers.

Defined in

Mathlib.CategoryTheory.Galois.Basic

Cited by

3 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreGaloisCategoryCategoryTheory.PreGaloisCategory.FiberFunctor