Theorems · Definition · category theory

CategoryTheory.IsPullback.isLimitKernelFork

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {X₁ X₂ X₃ X₄ : C} →
        [inst_2 : CategoryTheory.Limits.HasBinaryBiproduct X₂ X₃] →
          {fst : X₁ ⟶ X₂} →
            {snd : X₁ ⟶ X₃} →
              {f : X₂ ⟶ X₄} →
                {g : X₃ ⟶ X₄} → (h : CategoryTheory.IsPullback fst snd f g) → CategoryTheory.Limits.IsLimit ⋯.kernelFork

The limit kernel fork attached to a pullback square.

Defined in

Mathlib.Algebra.Homology.CommSq

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasBinaryBiproduct