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Theorems · Definition · category theory

CategoryTheory.ShortComplex.RightHomologyData.op

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      {S : CategoryTheory.ShortComplex C} → S.RightHomologyData → S.op.LeftHomologyData

A right homology data for a short complex S induces a left homology data for S.op.

Defined in
Mathlib.Algebra.Homology.ShortComplex.RightHomology
Cited by
17 results in Mathlib
Foundations
Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono · cited by 9RightHomologyData.ofEpiOf…CategoryTheory.ShortComplex.RightHomologyData.ofEpiOfIsIsoOfMono' · cited by 9RightHomologyData.ofEpiOf…CategoryTheory.ShortComplex.cyclesOpIso · cited by 8ShortComplex.cyclesOpIsoCategoryTheory.ShortComplex.HomologyData.op · cited by 7HomologyData.opCategoryTheory.ShortComplex.leftHomologyOpIso · cited by 4ShortComplex.leftHomology…CategoryTheory.ShortComplex.RightHomologyMapData.op · cited by 4RightHomologyMapData.opCategoryTheory.ShortComplex.cyclesOpIso_inv_op_iCycles · cited by 2ShortComplex.cyclesOpIso_…CategoryTheory.ShortComplex.fromOpcycles_op_cyclesOpIso_inv · cited by 2ShortComplex.fromOpcycles…CategoryTheory.ShortComplex.homologyMap_op · cited by 2ShortComplex.homologyMap_…CategoryTheory.ShortComplex.rightHomologyMap'_op · cited by 2ShortComplex.rightHomolog…CategoryTheory.ShortComplex.RightHomologyData.op_i · cited by 1RightHomologyData.op_iCategoryTheory.ShortComplex.RightHomologyMapData.op_φH · cited by 1RightHomologyMapData.op_φHCategoryTheory.ShortComplex.rightHomologyMap_op · cited by 0ShortComplex.rightHomolog…CategoryTheory.ShortComplex.RightHomologyData.op_H · cited by 0RightHomologyData.op_HCategoryTheory.ShortComplex.RightHomologyData.op_K · cited by 0RightHomologyData.op_KCategoryTheory.Category · cited by 32673CategoryTheory.CategoryOpposite · cited by 8081OppositeCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsQuiver.Hom.op · cited by 1948Hom.opCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.LeftHomologyData · cited by 212ShortComplex.LeftHomology…CategoryTheory.ShortComplex.RightHomologyData · cited by 211ShortComplex.RightHomolog…CategoryTheory.ShortComplex.RightHomologyData.Q · cited by 163RightHomologyData.QCategoryTheory.ShortComplex.RightHomologyData.H · cited by 158RightHomologyData.HCategoryTheory.ShortComplex.op · cited by 88ShortComplex.opCategoryTheory.ShortComplex.RightHomologyData.p · cited by 84RightHomologyData.pCategoryTheory.ShortComplex.RightHomologyData.ι · cited by 69RightHomologyData.ιCategoryTheory.ShortComplex.RightHomologyData.wp · cited by 6RightHomologyData.wpCategoryTheory.ShortComplex.RightHomologyData.hp · cited by 5RightHomologyData.hpCategoryTheory.ShortComplex.RightHomologyData.hι · cited by 3RightHomologyData.hιRightHomologyData.opCITED BYCITES

Cites18

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Cited by23

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