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Theorems · Definition · category theory

CategoryTheory.ShortComplex.op

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      CategoryTheory.ShortComplex C → CategoryTheory.ShortComplex Cᵒᵖ

The opposite ShortComplex in Cᵒᵖ associated to a short complex in C.

Defined in
Mathlib.Algebra.Homology.ShortComplex.Basic
Cited by
88 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

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

CategoryTheory.ShortComplex.opMap · cited by 42ShortComplex.opMapCategoryTheory.ShortComplex.RightHomologyData.op · cited by 17RightHomologyData.opCategoryTheory.ShortComplex.LeftHomologyData.op · cited by 13LeftHomologyData.opCategoryTheory.ShortComplex.SnakeInput.op · cited by 10SnakeInput.opCategoryTheory.ShortComplex.opFunctor · cited by 8ShortComplex.opFunctorCategoryTheory.ShortComplex.opcyclesOpIso · cited by 8ShortComplex.opcyclesOpIsoCategoryTheory.ShortComplex.cyclesOpIso · cited by 8ShortComplex.cyclesOpIsoCategoryTheory.ShortComplex.HomologyData.op · cited by 7HomologyData.opCategoryTheory.ShortComplex.Exact.op · cited by 5Exact.opCategoryTheory.ShortComplex.homologyOpIso · cited by 5ShortComplex.homologyOpIsoCategoryTheory.ShortComplex.HomologyMapData.op · cited by 4HomologyMapData.opCategoryTheory.ShortComplex.Homotopy.op · cited by 4Homotopy.opCategoryTheory.ShortComplex.leftHomologyOpIso · cited by 4ShortComplex.leftHomology…CategoryTheory.ShortComplex.RightHomologyMapData.op · cited by 4RightHomologyMapData.opCategoryTheory.ShortComplex.quasiIso_opMap_iff · cited by 4ShortComplex.quasiIso_opM…CategoryTheory.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.g · cited by 658ShortComplex.gCategoryTheory.ShortComplex.f · cited by 653ShortComplex.fShortComplex.opCITED BYCITES

Cites7

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Cited by107

Results whose statement or proof uses this declaration.