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Theorems · Definition · category theory

CategoryTheory.ShortComplex.unop

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

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

Defined in
Mathlib.Algebra.Homology.ShortComplex.Basic
Cited by
44 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.unopMap · cited by 16ShortComplex.unopMapCategoryTheory.ShortComplex.RightHomologyData.unop · cited by 10RightHomologyData.unopCategoryTheory.ShortComplex.LeftHomologyData.unop · cited by 10LeftHomologyData.unopCategoryTheory.ShortComplex.HomologyData.unop · cited by 6HomologyData.unopCategoryTheory.ShortComplex.Homotopy.unop · cited by 4Homotopy.unopCategoryTheory.ShortComplex.Exact.unop · cited by 4Exact.unopCategoryTheory.ShortComplex.unopFunctor · cited by 4ShortComplex.unopFunctorCategoryTheory.ShortComplex.RightHomologyMapData.unop · cited by 3RightHomologyMapData.unopCategoryTheory.ShortComplex.LeftHomologyMapData.unop · cited by 3LeftHomologyMapData.unopCategoryTheory.ShortComplex.HomologyMapData.unop · cited by 2HomologyMapData.unopCategoryTheory.ShortComplex.exact_unop_iff · cited by 2ShortComplex.exact_unop_i…CategoryTheory.ShortComplex.Splitting.unop · cited by 2Splitting.unopCategoryTheory.ShortComplex.quasiIso_iff_of_zeros' · cited by 2ShortComplex.quasiIso_iff…CategoryTheory.ShortComplex.ShortExact.unop · cited by 1ShortExact.unopCategoryTheory.ShortComplex.quasiIso_unopMap · cited by 0ShortComplex.quasiIso_uno…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryOpposite · cited by 8081OppositeCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…Quiver.Hom.unop · cited by 903Hom.unopCategoryTheory.ShortComplex.g · cited by 658ShortComplex.gCategoryTheory.ShortComplex.f · cited by 653ShortComplex.fShortComplex.unopCITED BYCITES

Cites7

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Cited by56

Results whose statement or proof uses this declaration.