Theorems · Theorem · category theory
HomologicalComplex.epi_homologyMap_of_epi_of_not_rel
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
{ι : Type u_2} {c : ComplexShape ι} {K L : HomologicalComplex C c} (φ : K ⟶ L) (i : ι) [inst_2 : K.HasHomology i]
[inst_3 : L.HasHomology i] [CategoryTheory.Epi (φ.f i)],
(∀ (j : ι), ¬c.Rel i j) → CategoryTheory.Epi (HomologicalComplex.homologyMap φ i)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 49 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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.compproof · cited by 17,999
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- HomologicalComplex.Xstatement · cited by 1,839
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- HomologicalComplex.Hom.fstatement and proof · cited by 845
- CategoryTheory.Epistatement and proof · cited by 688
- ComplexShape.Relstatement and proof · cited by 518
- HomologicalComplex.HasHomologystatement and proof · cited by 342
- ComplexShape.nextproof · cited by 297
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.ShortComplex.ShortExact.exactAt_X₃proof · cited by 1
- HomologicalComplex.HomologySequence.epi_homologyMap_τ₃proof · cited by 1
- HomologicalComplex.HomologySequence.mono_homologyMap_τ₃proof · cited by 1