Theorems · Theorem · category theory
CategoryTheory.CommSq.HasLift.iff_op
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {A B X Y : C} {f : A ⟶ X} {i : A ⟶ B} {p : X ⟶ Y}
{g : B ⟶ Y} (sq : CategoryTheory.CommSq f i p g), sq.HasLift ↔ ⋯.HasLift- Defined in
- Mathlib.CategoryTheory.CommSq
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Oppositestatement · cited by 8,081
- Quiver.Hom.opstatement · cited by 1,948
- Equiv.toFunproof · cited by 279
- Equiv.invFunproof · cited by 163
- CategoryTheory.CommSqstatement and proof · cited by 158
- CategoryTheory.CommSq.LiftStructproof · cited by 33
- CategoryTheory.CommSq.HasLiftstatement and proof · cited by 20
- Nonempty.congrproof · cited by 6
- CategoryTheory.CommSq.opstatement and proof · cited by 5
- CategoryTheory.CommSq.HasLift.iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.HasLiftingProperty.unopproof · cited by 2