Theorems · Inductive type · category theory
CategoryTheory.HasLiftingProperty
{C : Type u_1} → [inst : CategoryTheory.Category.{v_1, u_1} C] → {A B X Y : C} → (A ⟶ B) → (X ⟶ Y) → PropHasLiftingProperty i p means that i has the left lifting
property with respect to p, or equivalently that p has
the right lifting property with respect to i.
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- Quiver.Homstatement · cited by 32,603
Cited by65
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.rlpproof · cited by 53
- CategoryTheory.MorphismProperty.llpproof · cited by 40
- CategoryTheory.ParametrizedAdjunction.hasLiftingProperty_iffstatement · cited by 6
- CategoryTheory.HasLiftingProperty.iff_of_arrow_iso_leftstatement and proof · cited by 6
- CategoryTheory.Adjunction.hasLiftingProperty_iffstatement and proof · cited by 3
- CategoryTheory.HasLiftingProperty.iff_of_arrow_iso_rightstatement and proof · cited by 3
- CategoryTheory.SmallObject.llp_rlp_of_isCardinalForSmallObjectArgument'proof · cited by 3
- SSet.Quasicategory.hasLiftingPropertystatement · cited by 2
- CategoryTheory.Injective.hasLiftingProperty_of_isZerostatement · cited by 2
- CategoryTheory.HasLiftingProperty.of_arrow_iso_leftstatement and proof · cited by 2
- CategoryTheory.HasLiftingProperty.of_arrow_iso_rightstatement and proof · cited by 2
- CategoryTheory.HasLiftingProperty.opstatement and proof · cited by 2