Theorems · Theorem · category theory
CategoryTheory.Functor.essImage_comp_of_essSurj
∀ {C : Type u₁} {D : Type u₂} {E : Type u₃} [inst : CategoryTheory.Category.{v₁, u₁} C]
[inst_1 : CategoryTheory.Category.{v₂, u₂} D] [inst_2 : CategoryTheory.Category.{v₃, u₃} E]
{F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D E} [F.EssSurj], (F.comp G).essImage = G.essImagePre-composing by an essentially surjective functor doesn't change the essential image.
- Defined in
- Mathlib.CategoryTheory.EssentialImage
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.compstatement · cited by 6,529
- CategoryTheory.ObjectPropertystatement · cited by 798
- CategoryTheory.Functor.EssSurjstatement and proof · cited by 88
- CategoryTheory.Functor.essImagestatement · cited by 82
- CategoryTheory.Functor.essImage_comp_apply_of_essSurjproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.essImage_bialgSpecproof · cited by 0
- AlgebraicGeometry.essImage_hopfSpecproof · cited by 0
- AlgebraicGeometry.essImage_algSpecproof · cited by 0