Theorems · Definition · category theory

CategoryTheory.Limits.pullbackConeEquivBinaryFan

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      {f : Y ⟶ X} →
        {g : Z ⟶ X} →
          CategoryTheory.Limits.PullbackCone f g ≌
            CategoryTheory.Limits.BinaryFan (CategoryTheory.Over.mk f) (CategoryTheory.Over.mk g)

Pullback cones to X are the same thing as binary fans in Over X.

Defined in

Mathlib.CategoryTheory.Limits.Constructions.Over.Products

Cited by

23 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category