Theorems · Definition · category theory

CategoryTheory.Limits.PullbackCone.eta

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y Z : C} →
      {f : X ⟶ Z} →
        {g : Y ⟶ Z} →
          (t : CategoryTheory.Limits.PullbackCone f g) → t ≅ CategoryTheory.Limits.PullbackCone.mk t.fst t.snd ⋯

The natural isomorphism between a pullback cone and the corresponding pullback cone reconstructed using PullbackCone.mk.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone
Cited by: 5 results in Mathlib
Foundations: Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites14

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.Isostatement · cited by 3,963
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
CategoryTheory.Iso.reflproof · cited by 727
CategoryTheory.Limits.WalkingCospanstatement · cited by 496
CategoryTheory.Limits.cospanstatement · cited by 467
CategoryTheory.Limits.PullbackCone.mkstatement · cited by 203
CategoryTheory.Limits.PullbackConestatement and proof · cited by 136
CategoryTheory.Limits.PullbackCone.fststatement · cited by 118
CategoryTheory.Limits.PullbackCone.sndstatement · cited by 113

Cited by10

Results whose statement or proof uses this declaration.

AlgebraicGeometry.pullbackSpecIsoproof · cited by 26
CategoryTheory.Limits.pullbackConeEquivBinaryFanproof · cited by 23
AlgebraicGeometry.pullbackSpecIso_inv_fstproof · cited by 7
AlgebraicGeometry.pullbackSpecIso_inv_sndproof · cited by 6
CategoryTheory.Limits.pullbackConeEquivBinaryFan_unitIsostatement · cited by 0
CategoryTheory.TransitiveRelation.mapproof · cited by 0
CategoryTheory.Limits.PullbackCone.mkSelfIsLimitproof · cited by 0
CategoryTheory.Limits.PullbackCone.mkSelfIsWeakLimitproof · cited by 0
CategoryTheory.Limits.PullbackCone.eta_hom_homstatement and proof · cited by 0
CategoryTheory.Limits.PullbackCone.eta_inv_homstatement and proof · cited by 0