Theorems · Theorem · category theory
CategoryTheory.Functor.Full.map_surjective
∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {D : Type u₂} {inst_1 : CategoryTheory.Category.{v₂, u₂} D}
{F : CategoryTheory.Functor C D} [self : F.Full] {X Y : C}, Function.Surjective F.map- Cited by
- 3 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Functor.Full
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 · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement · cited by 8,698
- CategoryTheory.Functor.Fullstatement and proof · cited by 341
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.map_surjectiveproof · cited by 29
- CategoryTheory.Functor.mapExt_bijective_of_preservesInjectiveObjectsproof · cited by 0
- CategoryTheory.Functor.mapExt_bijective_of_preservesProjectiveObjectsproof · cited by 0