Theorems · Theorem · category theory
CategoryTheory.ObjectProperty.exists_comp_monoModSerre_eq_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} (f : X ⟶ Y),
(∃ Y' s, ∃ (_ : P.monoModSerre s), CategoryTheory.CategoryStruct.comp f s = 0) ↔ P (CategoryTheory.Abelian.image f)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- CategoryTheory.Limits.comp_zeroproof · cited by 365
- CategoryTheory.Limits.cokernelstatement and proof · cited by 229
- CategoryTheory.Limits.kernel.ιproof · cited by 214
- CategoryTheory.Limits.cokernel.πstatement and proof · cited by 194
- CategoryTheory.ObjectProperty.IsSerreClassstatement and proof · cited by 61
- CategoryTheory.Abelian.imagestatement and proof · cited by 57
- CategoryTheory.Limits.kernel.conditionproof · cited by 52
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.SerreClassLocalization.mono_map_tfaeproof · cited by 1
- CategoryTheory.ObjectProperty.exists_comp_isoModSerre_eq_zero_iffproof · cited by 1