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Theorems · Inductive type · category theory

CategoryTheory.MorphismProperty.ContainsIdentities

{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → Prop

Typeclass expressing that a morphism property contains identities.

Defined in
Mathlib.CategoryTheory.MorphismProperty.Composition
Cited by
94 results in Mathlib
Foundations
Depth 3 from the axioms, rests on 8 definitions · uses no axioms
Assumes
CategoryTheory.Category

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.MorphismProperty.id_mem · cited by 23MorphismProperty.id_memAlgebraicGeometry.Scheme.coverOfIsIso · cited by 9Scheme.coverOfIsIsoCategoryTheory.MorphismProperty.LeftFraction.ofHom · cited by 8LeftFraction.ofHomCategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost · cited by 6Monoidal.curriedTensorPre…AlgebraicGeometry.IsZariskiLocalAtSource.of_isOpenImmersion · cited by 5IsZariskiLocalAtSource.of…CategoryTheory.MorphismProperty.RightFraction.ofHom · cited by 5RightFraction.ofHomCategoryTheory.MorphismProperty.of_isIso · cited by 5MorphismProperty.of_isIsoCategoryTheory.Localization.Monoidal.functorCoreMonoidalOfComp · cited by 5Monoidal.functorCoreMonoi…CategoryTheory.MorphismProperty.underEquivOfIsTerminal · cited by 4MorphismProperty.underEqu…CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prodLift₁ · cited by 4StrictUniversalPropertyFi…AlgebraicGeometry.Scheme.Cover.pushforwardIso · cited by 4Cover.pushforwardIsoCategoryTheory.MorphismProperty.ContainsIdentities.id_mem · cited by 4ContainsIdentities.id_memCategoryTheory.Localization.lift₂NatTrans · cited by 4Localization.lift₂NatTransCategoryTheory.Localization.lift₃NatTrans · cited by 4Localization.lift₃NatTransCategoryTheory.MorphismProperty.overEquivOfIsInitial · cited by 4MorphismProperty.overEqui…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…MorphismProperty.ContainsIden…CITED BYCITES

Cites2

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

Cited by125

Results whose statement or proof uses this declaration.