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Theorems · Theorem · category theory

HomologicalComplex.cyclesMap_id

∀ {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 : HomologicalComplex C c) (i : ι) [inst_2 : K.HasHomology i],
  HomologicalComplex.cyclesMap (CategoryTheory.CategoryStruct.id K) i = CategoryTheory.CategoryStruct.id (K.cycles i)
Defined in
Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
Cited by
3 results in Mathlib
Foundations
Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsHomologicalComplex.HasHomology
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

groupCohomology.cocyclesMap_id · cited by 0groupCohomology.cocyclesM…ContinuousCohomology.cocyclesMap_id · cited by 0ContinuousCohomology.cocy…groupHomology.cyclesMap_id · cited by 0groupHomology.cyclesMap_idCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsHomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeHomologicalComplex.HasHomology · cited by 342HomologicalComplex.HasHom…HomologicalComplex.sc · cited by 205HomologicalComplex.scHomologicalComplex.cycles · cited by 164HomologicalComplex.cyclesHomologicalComplex.cyclesMap · cited by 59HomologicalComplex.cycles…CategoryTheory.ShortComplex.cyclesMap_id · cited by 1ShortComplex.cyclesMap_idHomologicalComplex.cyclesMap_…CITED BYCITES

Cites11

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Cited by3

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