Theorems · Theorem · category theory
CategoryTheory.Functor.preservesMonomorphisms_of_adjunction_of_preservesInjectiveObjects
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
[CategoryTheory.EnoughInjectives D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (adj : F ⊣ G)
[G.PreservesInjectiveObjects], F.PreservesMonomorphisms- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Monoproof · cited by 893
- CategoryTheory.Functor.map_compproof · cited by 734
- CategoryTheory.Adjunctionstatement and proof · cited by 524
- CategoryTheory.Adjunction.unitproof · cited by 387
Cited by1
Results whose statement or proof uses this declaration.