Theorems · Theorem · category theory
CochainComplex.next
∀ (α : Type u_2) [inst : AddRightCancelSemigroup α] [inst_1 : One α] (i : α), (ComplexShape.up α).next i = i + 1
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddRightCancelSemigroupOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ComplexShape.upstatement and proof · cited by 1,123
- ComplexShape.nextstatement · cited by 297
- ComplexShape.next_eq'proof · cited by 48
- AddRightCancelSemigroupstatement and proof · cited by 41
Cited by13
Results whose statement or proof uses this declaration.
- groupCohomology.δ_applyproof · cited by 2
- CategoryTheory.InjectiveResolution.exact_succproof · cited by 2
- CochainComplex.isKInjective_of_injective_auxproof · cited by 1
- CochainComplex.isSplitEpi_to_singleFunctor_obj_of_projectiveproof · cited by 1
- CochainComplex.injective_opcyclesproof · cited by 1
- CochainComplex.exactAt_opproof · cited by 1
- CochainComplex.mappingCone.homologySequenceδ_trianglehproof · cited by 1
- groupCohomology.iCocycles_mkproof · cited by 1
- ComplexShape.boundaryLE_embeddingUpIntLE_iffproof · cited by 0
- Homotopy.dNext_cochainComplexproof · cited by 0
- CochainComplex.quasiIsoAt₀_iffproof · cited by 0
- CochainComplex.isIso_liftCycles_iffproof · cited by 0