Theorems · Theorem · category theory
CategoryTheory.CommSq.HasLift.iff
∀ {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 ↔ Nonempty sq.LiftStruct- Defined in
- Mathlib.CategoryTheory.CommSq
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.CommSqstatement and proof · cited by 158
- CategoryTheory.CommSq.LiftStructstatement and proof · cited by 33
- CategoryTheory.CommSq.HasLiftstatement and proof · cited by 20
- CategoryTheory.CommSq.HasLift.exists_liftproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.CommSq.HasLift.iff_opproof · cited by 1
- CategoryTheory.CommSq.left_adjoint_hasLift_iffproof · cited by 1
- CategoryTheory.CommSq.HasLift.iff_unopproof · cited by 0