Theorems · Inductive type · category theory
CategoryTheory.MorphismProperty.ContainsIdentities
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.MorphismProperty C → PropTypeclass expressing that a morphism property contains identities.
- 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.
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
- CategoryTheory.MorphismPropertystatement · cited by 2,179
Cited by125
Results whose statement or proof uses this declaration.
- CategoryTheory.MorphismProperty.id_memstatement and proof · cited by 23
- AlgebraicGeometry.Scheme.coverOfIsIsostatement and proof · cited by 9
- CategoryTheory.MorphismProperty.LeftFraction.ofHomstatement and proof · cited by 8
- CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPoststatement and proof · cited by 6
- AlgebraicGeometry.IsZariskiLocalAtSource.of_isOpenImmersionstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.RightFraction.ofHomstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.of_isIsostatement and proof · cited by 5
- CategoryTheory.Localization.Monoidal.functorCoreMonoidalOfCompstatement and proof · cited by 5
- CategoryTheory.MorphismProperty.underEquivOfIsTerminalstatement and proof · cited by 4
- CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.prodLift₁statement and proof · cited by 4
- AlgebraicGeometry.Scheme.Cover.pushforwardIsostatement and proof · cited by 4
- CategoryTheory.MorphismProperty.ContainsIdentities.id_memstatement and proof · cited by 4