Theorems · Theorem · category theory

CategoryTheory.Functor.injective_of_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) [F.Full] [F.Faithful]
  [F.PreservesMonomorphisms] {I : C}, CategoryTheory.Injective (F.obj I) → CategoryTheory.Injective I

Defined in: Mathlib.CategoryTheory.Preadditive.Injective.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 11 from the axioms · uses propext, Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Functor.Full CategoryTheory.Functor.Faithful CategoryTheory.Functor.PreservesMonomorphisms

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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.Monoproof · cited by 893
CategoryTheory.Functor.map_compproof · cited by 734
CategoryTheory.Functor.Fullstatement and proof · cited by 341
CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
CategoryTheory.Functor.map_injectiveproof · cited by 91
CategoryTheory.Injectivestatement and proof · cited by 70

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