Theorems · Theorem · category theory
CategoryTheory.Limits.pullback.lift_fst_snd
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y Z : C} (f : X ⟶ Z) (g : Y ⟶ Z)
[inst_1 : CategoryTheory.Limits.HasPullback f g],
CategoryTheory.Limits.pullback.lift (CategoryTheory.Limits.pullback.fst f g) (CategoryTheory.Limits.pullback.snd f g)
⋯ =
CategoryTheory.CategoryStruct.id (CategoryTheory.Limits.pullback f g)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.idstatement · cited by 6,235
- CategoryTheory.Category.id_compproof · cited by 1,998
- CategoryTheory.Limits.pullbackstatement · cited by 864
- CategoryTheory.Limits.pullback.fststatement and proof · cited by 639
- CategoryTheory.Limits.pullback.sndstatement and proof · cited by 637
- CategoryTheory.Limits.HasPullbackstatement and proof · cited by 434
- CategoryTheory.Limits.limit.lift_πproof · cited by 266
- CategoryTheory.Limits.PullbackCone.mkproof · cited by 203
- CategoryTheory.Limits.WalkingCospan.leftproof · cited by 190
- CategoryTheory.Limits.WalkingCospan.rightproof · cited by 182
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.PreOneHypercover.sieve₁'_eq_sieve₁proof · cited by 2
- CategoryTheory.sieve₁'_toPreOneHypercover_eq_topproof · cited by 0