Theorems · Definition · category theory
CategoryTheory.Functor.toEssImage
{C : Type u₁} →
{D : Type u₂} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
(F : CategoryTheory.Functor C D) → CategoryTheory.Functor C F.EssImageSubcategoryGiven a functor F : C ⥤ D, we have an (essentially surjective) functor from C to the essential
image of F.
- Defined in
- Mathlib.CategoryTheory.EssentialImage
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 17 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
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.essImagestatement and proof · cited by 82
- CategoryTheory.ObjectProperty.liftproof · cited by 33
- CategoryTheory.Functor.EssImageSubcategorystatement · cited by 19
- CategoryTheory.Functor.obj_mem_essImageproof · cited by 7
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.equivEssImageOfReflectiveproof · cited by 4
- CategoryTheory.Functor.essImage.liftFunctorproof · cited by 4
- CategoryTheory.Functor.essImage.liftFunctorCompIsoproof · cited by 2
- CategoryTheory.Functor.toEssImageCompιstatement · cited by 2
- CategoryTheory.equivEssImageOfReflective_counitIsostatement · cited by 0
- CategoryTheory.equivEssImageOfReflective_functorstatement · cited by 0
- CategoryTheory.Functor.essImage.liftFunctorCompIso_hom_appstatement · cited by 0
- CategoryTheory.Functor.essImage.liftFunctorCompIso_inv_appstatement · cited by 0
- CategoryTheory.Functor.essImage.liftFunctor_mapstatement · cited by 0
- CategoryTheory.Functor.essImage.liftFunctor_objstatement · cited by 0
- AlgebraicGeometry.AffineScheme.Specproof · cited by 0
- CategoryTheory.Functor.toEssImageCompι_hom_appstatement · cited by 0