Theorems · Theorem · category theory

CochainComplex.Plus.mono_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [CategoryTheory.Limits.HasLimitsOfShape CategoryTheory.Limits.WalkingCospan C] {X Y : CochainComplex.Plus C}
  (f : X ⟶ Y), CategoryTheory.Mono f ↔ CategoryTheory.Mono f.hom

Defined in: Mathlib.Algebra.Homology.CochainComplexPlus
Cited by: 0 results in Mathlib
Foundations: Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasLimitsOfShape

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.WalkingPairstatement · cited by 1,319
CategoryTheory.ObjectProperty.FullSubcategory.objstatement · cited by 1,316
ComplexShape.upstatement · cited by 1,123
CochainComplexstatement · cited by 1,016
CategoryTheory.Monostatement and proof · cited by 893
CategoryTheory.InducedCategory.Hom.homstatement and proof · cited by 850
CategoryTheory.ObjectProperty.FullSubcategorystatement · cited by 726
CategoryTheory.Limits.WalkingCospanstatement and proof · cited by 496
CategoryTheory.Limits.HasLimitsOfShapestatement and proof · cited by 223

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