Theorems · Theorem · category theory

CategoryTheory.Adjunction.map_injective

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u_1}
  [inst_1 : CategoryTheory.Category.{v_1, u_1} D] {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C}
  (adj : F ⊣ G) [F.PreservesMonomorphisms] (I : D), CategoryTheory.Injective I → CategoryTheory.Injective (G.obj I)

Defined in: Mathlib.CategoryTheory.Preadditive.Injective.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.PreservesMonomorphisms

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Cites18

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.objstatement and proof · 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.comp_idproof · cited by 2,119
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 by2

Results whose statement or proof uses this declaration.

CategoryTheory.Equivalence.map_injective_iffproof · cited by 1
CategoryTheory.Functor.preservesInjectiveObjects_of_adjunction_of_preservesMonomorphismsproof · cited by 0