Theorems · Definition · category theory
CategoryTheory.Limits.PullbackCone
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X Y Z : C} → (X ⟶ Z) → (Y ⟶ Z) → Type (max (max 0 u) v)A pullback cone is just a cone on the cospan formed by two morphisms f : X ⟶ Z and
g : Y ⟶ Z.
- Cited by
- 136 results in Mathlib
- Foundations
- Depth 17 from the axioms, rests on 87 definitions · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Limits.Coneproof · cited by 710
- CategoryTheory.Limits.cospanproof · cited by 467
Cited by256
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.PullbackCone.mkstatement · cited by 203
- CategoryTheory.Limits.PullbackCone.fststatement and proof · cited by 118
- CategoryTheory.Limits.PullbackCone.sndstatement and proof · cited by 113
- CategoryTheory.Limits.PullbackCone.conditionstatement and proof · cited by 44
- CategoryTheory.Limits.pullbackConeEquivBinaryFanstatement and proof · cited by 23
- CategoryTheory.Limits.pullback.conestatement · cited by 18
- CategoryTheory.IsPullback.conestatement · cited by 16
- CategoryTheory.Limits.PullbackCone.IsLimit.liftstatement and proof · cited by 15
- CategoryTheory.Limits.PullbackCone.IsLimit.mkstatement and proof · cited by 14
- CategoryTheory.Limits.IsLimit.pullbackConeEquivBinaryFanFunctorstatement and proof · cited by 13
- CategoryTheory.IsPullback.of_isLimitstatement and proof · cited by 12
- CategoryTheory.Limits.PullbackCone.IsLimit.lift_fststatement and proof · cited by 12
Showing the 200 most cited of 256.