Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.monoModSerre_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  (P : CategoryTheory.ObjectProperty C) [inst_2 : P.IsSerreClass] {X Y : C} (f : X ⟶ Y),
  P.monoModSerre f ↔ P (CategoryTheory.Limits.kernel f)

Defined in: Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty
Cited by: 0 results in Mathlib
Foundations: Depth 23 from the axioms · uses propext, Classical.choice
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.ObjectProperty.IsSerreClass

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CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.ObjectPropertystatement and proof · cited by 798
CategoryTheory.Limits.kernelstatement · cited by 272
CategoryTheory.ObjectProperty.IsSerreClassstatement and proof · cited by 61
CategoryTheory.ObjectProperty.monoModSerrestatement · cited by 16

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