Theorems · Theorem · category theory
CategoryTheory.Abelian.Ext.eq_zero_of_projective
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
[inst_2 : CategoryTheory.HasExt C] {P Y : C} {n : ℕ} [CategoryTheory.Projective P]
(e : CategoryTheory.Abelian.Ext P Y (n + 1)), e = 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.NatTrans.appproof · cited by 7,406
- CategoryTheory.Functor.compproof · cited by 6,529
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.shiftFunctorproof · cited by 1,553
- Equiv.injectiveproof · cited by 464
- CategoryTheory.cancel_monoproof · cited by 435
Cited by4
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Ext.subsingleton_of_projectiveproof · cited by 1
- precomp_extClass_surjective_of_projective_X₂proof · cited by 0
- CategoryTheory.hasExt_of_enoughProjectivesproof · cited by 0
- CategoryTheory.hasInjectiveDimensionLT_of_enoughProjectivesproof · cited by 0