Theorems · Definition · category theory

CategoryTheory.Limits.Image.imageFactorisation

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {X Y : C} → (f : X ⟶ Y) → [CategoryTheory.Limits.HasImage f] → CategoryTheory.Limits.ImageFactorisation f

Some image factorisation of f through a monomorphism (selected with choice).

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Images
Cited by: 0 results in Mathlib
Foundations: Depth 4 from the axioms · uses Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasImage

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites5

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.Limits.HasImagestatement and proof · cited by 107
CategoryTheory.Limits.ImageFactorisationstatement · cited by 11
CategoryTheory.Limits.HasImage.exists_imageproof · cited by 1

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.Image.monoFactorisationproof · cited by 15
CategoryTheory.Limits.Image.isImageproof · cited by 11
CategoryTheory.Subobject.imageFactorisationproof · cited by 4