Theorems · Theorem · category theory
CategoryTheory.IsPullback.op
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {P X Y Z : C} {fst : P ⟶ X} {snd : P ⟶ Y} {f : X ⟶ Z}
{g : Y ⟶ Z}, CategoryTheory.IsPullback fst snd f g → CategoryTheory.IsPushout g.op f.op snd.op fst.op- Cited by
- 5 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
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.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- Oppositestatement · cited by 8,081
- Quiver.Hom.opstatement · cited by 1,948
- CategoryTheory.IsPullbackstatement and proof · cited by 320
- CategoryTheory.IsPushoutstatement · cited by 219
- CategoryTheory.IsPullback.flipproof · cited by 61
- CategoryTheory.IsPullback.toCommSqproof · cited by 52
- CategoryTheory.IsPullback.isLimitproof · cited by 47
- CategoryTheory.Limits.IsColimit.ofIsoColimitproof · cited by 45
- CategoryTheory.IsPullback.coneproof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.NatTrans.Equifibered.opproof · cited by 2
- CategoryTheory.IsPushout.op_iffproof · cited by 0
- CategoryTheory.NatTrans.Equifibered.rightOpproof · cited by 0
- CategoryTheory.Square.IsPullback.opproof · cited by 0
- CategoryTheory.IsPullback.unop_iffproof · cited by 0