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Theorems · Definition · category theory

CategoryTheory.RegularMono.ofIsSplitMono

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {X Y : C} → (f : X ⟶ Y) → [CategoryTheory.IsSplitMono f] → CategoryTheory.RegularMono f

Every split monomorphism is a regular monomorphism.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.RegularMono
Cited by
0 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.IsSplitMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

CategoryTheory.HasSubobjectClassifier.truthIsRegularMono · cited by 0HasSubobjectClassifier.tr…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.IsSplitMono · cited by 33CategoryTheory.IsSplitMonoCategoryTheory.retraction · cited by 14CategoryTheory.retractionCategoryTheory.RegularMono · cited by 14CategoryTheory.RegularMonoCategoryTheory.Limits.isSplitMonoEqualizes · cited by 0Limits.isSplitMonoEqualiz…RegularMono.ofIsSplitMonoCITED BYCITES

Cites8

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Cited by1

Results whose statement or proof uses this declaration.