Theorems · Definition · category theory
CategoryTheory.Abelian.imageStrongEpiMonoFactorisation
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
[CategoryTheory.Abelian C] → {P Q : C} → (f : P ⟶ Q) → CategoryTheory.Limits.StrongEpiMonoFactorisation fFactoring through the image is a strong epi-mono factorisation.
- Defined in
- Mathlib.CategoryTheory.Abelian.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.Abelian.imageproof · cited by 57
- CategoryTheory.Abelian.image.ιproof · cited by 25
- CategoryTheory.Abelian.factorThruImageproof · cited by 20
- CategoryTheory.Limits.StrongEpiMonoFactorisationstatement · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.imageIsoImageproof · cited by 4
- CategoryTheory.Abelian.imageStrongEpiMonoFactorisation_estatement and proof · cited by 1
- CategoryTheory.Abelian.imageStrongEpiMonoFactorisation_mstatement and proof · cited by 1
- CategoryTheory.Abelian.imageIsoImage_hom_comp_image_ιproof · cited by 1
- CategoryTheory.Abelian.imageStrongEpiMonoFactorisation_Istatement and proof · cited by 0
- CategoryTheory.Abelian.imageIsoImage_invproof · cited by 0