Theorems · Inductive type · category theory
CategoryTheory.RegularMono
{C : Type u₁} → [inst : CategoryTheory.Category.{v₁, u₁} C] → {X Y : C} → (X ⟶ Y) → Type (max u₁ v₁)A regular monomorphism is a morphism which is the equalizer of some parallel pair.
- Cited by
- 14 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 by47
Results whose statement or proof uses this declaration.
- CategoryTheory.IsRegularMono.regularMonostatement · cited by 4
- CategoryTheory.RegularMono.Zstatement and proof · cited by 3
- CategoryTheory.RegularMono.leftstatement and proof · cited by 3
- CategoryTheory.RegularMono.rightstatement and proof · cited by 3
- CategoryTheory.RegularMono.wstatement and proof · cited by 3
- CategoryTheory.LiftRightAdjoint.constructRightAdjointEquivstatement and proof · cited by 3
- CategoryTheory.RegularEpi.opstatement · cited by 2
- CategoryTheory.RegularEpi.unopstatement · cited by 2
- CategoryTheory.RegularMono.opstatement and proof · cited by 2
- CategoryTheory.RegularMono.unopstatement and proof · cited by 2
- CategoryTheory.LiftRightAdjoint.unitEqualisesstatement and proof · cited by 2
- CommRingCat.regularMonoOfFaithfullyFlatstatement · cited by 1