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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) → Prop

HasLiftingProperty 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.

Defined in
Mathlib.CategoryTheory.LiftingProperties.Basic
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.

CategoryTheory.MorphismProperty.rlp · cited by 53MorphismProperty.rlpCategoryTheory.MorphismProperty.llp · cited by 40MorphismProperty.llpCategoryTheory.ParametrizedAdjunction.hasLiftingProperty_iff · cited by 6ParametrizedAdjunction.ha…CategoryTheory.HasLiftingProperty.iff_of_arrow_iso_left · cited by 6HasLiftingProperty.iff_of…CategoryTheory.Adjunction.hasLiftingProperty_iff · cited by 3Adjunction.hasLiftingProp…CategoryTheory.HasLiftingProperty.iff_of_arrow_iso_right · cited by 3HasLiftingProperty.iff_of…CategoryTheory.SmallObject.llp_rlp_of_isCardinalForSmallObjectArgument' · cited by 3SmallObject.llp_rlp_of_is…SSet.Quasicategory.hasLiftingProperty · cited by 2Quasicategory.hasLiftingP…CategoryTheory.Injective.hasLiftingProperty_of_isZero · cited by 2Injective.hasLiftingPrope…CategoryTheory.HasLiftingProperty.of_arrow_iso_left · cited by 2HasLiftingProperty.of_arr…CategoryTheory.HasLiftingProperty.of_arrow_iso_right · cited by 2HasLiftingProperty.of_arr…CategoryTheory.HasLiftingProperty.op · cited by 2HasLiftingProperty.opCategoryTheory.HasLiftingProperty.unop · cited by 2HasLiftingProperty.unopCategoryTheory.MonoidalCategory.Arrow.PushoutProduct.hasLiftingProperty_mk_iff · cited by 2PushoutProduct.hasLifting…CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.hasLiftingProperty_mk_isInitial_iff · cited by 2PushoutProduct.hasLifting…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.HasLiftingProp…CITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by65

Results whose statement or proof uses this declaration.