Theorems · Definition · category theory

CategoryTheory.Limits.PullbackCone.snd

{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.pt ⟶ Y

The second projection of a pullback cone.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone
Cited by: 113 results in Mathlib
Foundations: Depth 23 from the axioms, rests on 142 definitions · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category

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Cites10

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.NatTrans.appproof · cited by 7,406
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.Limits.Cone.ptstatement · cited by 1,298
CategoryTheory.Limits.Cone.πproof · cited by 500
CategoryTheory.Limits.WalkingCospanstatement · cited by 496
CategoryTheory.Limits.cospanstatement · cited by 467
CategoryTheory.Limits.WalkingCospan.rightproof · cited by 182
CategoryTheory.Limits.PullbackConestatement and proof · cited by 136

Cited by177

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.PullbackCone.conditionstatement · cited by 44
AlgebraicGeometry.pullbackSpecIsoproof · cited by 26
CategoryTheory.Limits.pullbackConeEquivBinaryFanproof · cited by 23
CategoryTheory.Limits.PullbackCone.IsLimit.mkstatement and proof · cited by 14
CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctorproof · cited by 13
CategoryTheory.IsPullback.of_isLimitstatement and proof · cited by 12
CategoryTheory.Limits.PullbackCone.IsLimit.lift_sndstatement · cited by 12
CategoryTheory.Limits.PullbackCone.IsLimit.hom_extstatement and proof · cited by 11
CategoryTheory.Limits.FormalCoproduct.pullbackConeproof · cited by 10
CategoryTheory.regularTopology.equalizerCondition_wstatement and proof · cited by 7
AlgebraicGeometry.pullbackSpecIso_inv_fstproof · cited by 7
CategoryTheory.Limits.pasteHorizIsPullbackproof · cited by 6