Theorems · Definition · category theory

CategoryTheory.Limits.isLimitMapConeBinaryFanEquiv

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (G : CategoryTheory.Functor C D) →
          {P X Y : C} →
            (f : P ⟶ X) →
              (g : P ⟶ Y) →
                CategoryTheory.Limits.IsLimit (G.mapCone (CategoryTheory.Limits.BinaryFan.mk f g)) ≃
                  CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.BinaryFan.mk (G.map f) (G.map g))

The map of a binary fan is a limit iff the fork consisting of the mapped morphisms is a limit. This essentially lets us commute BinaryFan.mk with Functor.mapCone.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.BinaryProducts

Cited by

1 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category