Theorems · Theorem · category theory

CategoryTheory.ObjectProperty.epiModSerre_zero_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), P.epiModSerre 0 ↔ P Y

Defined in: Mathlib.CategoryTheory.Abelian.SerreClass.MorphismProperty
Cited by: 1 results in Mathlib
Foundations: Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.ObjectProperty.IsSerreClass

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Cites8

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.Homstatement · cited by 32,603
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.ObjectPropertystatement and proof · cited by 798
CategoryTheory.ObjectProperty.IsSerreClassstatement and proof · cited by 61
CategoryTheory.ObjectProperty.epiModSerrestatement · cited by 16
CategoryTheory.ObjectProperty.prop_iff_of_isoproof · cited by 13
CategoryTheory.Limits.cokernelZeroIsoTargetproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.ObjectProperty.exists_epiModSerre_comp_eq_zero_iffproof · cited by 2