Theorems · Theorem · category theory
CategoryTheory.Functor.EssSurj.mem_essImage
∀ {C : Type u₁} {D : Type u₂} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.Category.{v₂, u₂} D}
(F : CategoryTheory.Functor C D) [self : F.EssSurj] (Y : D), F.essImage YAll the objects of the target category are in the essential image.
- Defined in
- Mathlib.CategoryTheory.EssentialImage
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.EssSurjstatement and proof · cited by 88
- CategoryTheory.Functor.essImagestatement · cited by 82
Cited by16
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.objObjPreimageIsoproof · cited by 54
- CategoryTheory.Functor.objPreimageproof · cited by 49
- CategoryTheory.LocalizerMorphism.hasLeftResolutions_of_iso_of_essSurjproof · cited by 2
- CategoryTheory.LocalizerMorphism.hasRightResolutions_of_iso_of_essSurjproof · cited by 2
- UnivLE.ofEssSurjproof · cited by 1
- CategoryTheory.ObjectProperty.SerreClassLocalization.hasCokernelsproof · cited by 1
- CategoryTheory.ObjectProperty.SerreClassLocalization.hasKernelsproof · cited by 1
- CategoryTheory.Functor.essImage_comp_apply_of_essSurjproof · cited by 1