Theorems · Definition · category theory
CategoryTheory.Limits.imageSubobject
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y : C} → (f : X ⟶ Y) → [CategoryTheory.Limits.HasImage f] → CategoryTheory.Subobject YThe image of a morphism f g : X ⟶ Y as a Subobject Y.
- Defined in
- Mathlib.CategoryTheory.Subobject.Limits
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Subobjectstatement · cited by 385
- CategoryTheory.Subobject.mkproof · cited by 109
- CategoryTheory.Limits.HasImagestatement and proof · cited by 107
- CategoryTheory.Limits.image.ιproof · cited by 104
Cited by58
Results whose statement or proof uses this declaration.
- imageToKernelstatement and proof · cited by 21
- CategoryTheory.Limits.imageSubobjectIsostatement · cited by 19
- imageToKernel_arrowstatement and proof · cited by 15
- CategoryTheory.Limits.factorThruImageSubobjectstatement · cited by 8
- CategoryTheory.Limits.imageSubobject_arrow'statement · cited by 7
- CategoryTheory.Limits.imageSubobjectCompIsostatement · cited by 6
- CategoryTheory.Limits.imageSubobject_arrowstatement and proof · cited by 6
- CategoryTheory.Limits.imageSubobjectMapstatement · cited by 5
- CategoryTheory.Limits.imageSubobject_arrow_compstatement and proof · cited by 5
- CategoryTheory.Limits.imageSubobject_arrow_assocstatement and proof · cited by 3
- CategoryTheory.Limits.imageSubobject_comp_lestatement · cited by 3
- CategoryTheory.Limits.imageSubobjectMap_arrowstatement and proof · cited by 2