Theorems · Definition · category theory

CategoryTheory.Limits.isLimitPrecompFork

{C : Type u} →
  {X Y : C} →
    [inst : CategoryTheory.Category.{v, u} C] →
      {f g : X ⟶ Y} →
        {Z : C} →
          (h : Z ⟶ X) →
            {s : CategoryTheory.Limits.Fork f g} →
              CategoryTheory.Limits.IsLimit s →
                {c : CategoryTheory.Limits.PullbackCone s.ι h} →
                  CategoryTheory.Limits.IsLimit c →
                    CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.precompFork h s c)

The pullback of an equalizer is an equalizer.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Equalizers
Cited by: 1 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.parallelPairstatement · cited by 766
CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
CategoryTheory.Limits.WalkingCospanstatement · cited by 496
CategoryTheory.Limits.cospanstatement · cited by 467
CategoryTheory.Limits.Fork.ιstatement and proof · cited by 162
CategoryTheory.Limits.PullbackConestatement and proof · cited by 136

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.hasEqualizer_precomp_of_equalizerproof · cited by 0