Theorems · Theorem · category theory

CategoryTheory.injective_iff_rlp_monomorphisms_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] (I : C),
  CategoryTheory.Injective I ↔ (CategoryTheory.MorphismProperty.monomorphisms C).rlp 0

Defined in: Mathlib.CategoryTheory.Preadditive.Injective.LiftingProperties
Cited by: 0 results in Mathlib
Foundations: Depth 13 from the axioms · uses propext, Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasZeroObject

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.Limits.HasZeroObject.zero'statement · cited by 115
CategoryTheory.Injectivestatement · cited by 70
CategoryTheory.MorphismProperty.rlpstatement · cited by 53
CategoryTheory.MorphismProperty.monomorphismsstatement · cited by 39
CategoryTheory.Limits.isZero_zeroproof · cited by 34
CategoryTheory.injective_iff_rlp_monomorphisms_of_isZeroproof · cited by 1

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