Theorems · Definition · category theory
CategoryTheory.Limits.image
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] → {X Y : C} → (f : X ⟶ Y) → [CategoryTheory.Limits.HasImage f] → CThe categorical image of a morphism.
- Cited by
- 124 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 15 definitions · uses Classical.choice
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.MonoFactorisation.Iproof · cited by 83
- CategoryTheory.Limits.Image.monoFactorisationproof · cited by 15
Cited by165
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.image.ιstatement · cited by 104
- CategoryTheory.Limits.factorThruImagestatement · cited by 55
- CategoryTheory.Limits.image.facstatement · cited by 27
- CategoryTheory.Limits.imageSubobjectIsostatement · cited by 19
- CategoryTheory.Limits.image.liftstatement · cited by 16
- CategoryTheory.Limits.image.lift_facstatement · cited by 10
- CategoryTheory.Limits.image.mapstatement · cited by 10
- CategoryTheory.PreservesImage.isostatement and proof · cited by 9
- CategoryTheory.Limits.ImageMap.mapstatement · cited by 9
- CategoryTheory.Limits.image.compIsostatement · cited by 7
- CategoryTheory.Limits.image.preCompstatement and proof · cited by 7
- CategoryTheory.Limits.imageSubobject_arrow'statement · cited by 7