Theorems · Definition · category theory
CategoryTheory.Limits.imageSubobjectIso
{C : Type u} →
[inst : CategoryTheory.Category.{v, u} C] →
{X Y : C} →
(f : X ⟶ Y) →
[inst_1 : CategoryTheory.Limits.HasImage f] →
CategoryTheory.Subobject.underlying.obj (CategoryTheory.Limits.imageSubobject f) ≅
CategoryTheory.Limits.image fThe underlying object of imageSubobject f is (up to isomorphism!)
the same as the chosen object image f.
- Defined in
- Mathlib.CategoryTheory.Subobject.Limits
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.Functor.objstatement · cited by 19,642
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Subobject.underlyingstatement · cited by 211
- CategoryTheory.Limits.imagestatement · cited by 124
- CategoryTheory.Limits.HasImagestatement and proof · cited by 107
- CategoryTheory.Limits.image.ιproof · cited by 104
- CategoryTheory.Limits.imageSubobjectstatement · cited by 53
- CategoryTheory.Subobject.underlyingIsoproof · cited by 41
Cited by22
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.factorThruImageSubobjectproof · cited by 8
- CategoryTheory.Limits.imageSubobject_arrow'statement · cited by 7
- CategoryTheory.Limits.imageSubobjectCompIsoproof · cited by 6
- CategoryTheory.Limits.imageSubobject_arrowstatement · cited by 6
- CategoryTheory.Limits.imageSubobjectMapproof · cited by 5
- CategoryTheory.Limits.imageSubobject_arrow_compproof · cited by 5
- CategoryTheory.Limits.imageSubobject_arrow_assocstatement and proof · cited by 3
- CategoryTheory.Limits.imageSubobjectMap_arrowproof · cited by 2
- CategoryTheory.Limits.imageSubobject_zero_arrowproof · cited by 2
- CategoryTheory.Limits.imageSubobjectCompIso_hom_arrowproof · cited by 1
- CategoryTheory.Limits.imageSubobjectCompIso_inv_arrowproof · cited by 1
- CategoryTheory.Limits.imageSubobject_arrow'_assocstatement and proof · cited by 1