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Theorems · Theorem · category theory

CategoryTheory.ShortComplex.RightHomologyData.p_descQ

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S : CategoryTheory.ShortComplex C} (h : S.RightHomologyData) {A : C} (k : S.X₂ ⟶ A)
  (hk : CategoryTheory.CategoryStruct.comp S.f k = 0), CategoryTheory.CategoryStruct.comp h.p (h.descQ k hk) = k
Defined in
Mathlib.Algebra.Homology.ShortComplex.RightHomology
Cited by
8 results in Mathlib
Foundations
Depth 27 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.p_g' · cited by 17RightHomologyData.p_g'CategoryTheory.ShortComplex.p_descOpcycles · cited by 9ShortComplex.p_descOpcycl…CategoryTheory.ShortComplex.RightHomologyData.p_descQ_assoc · cited by 2RightHomologyData.p_descQ…CategoryTheory.ShortComplex.RightHomologyData.isIso_p · cited by 2RightHomologyData.isIso_pCategoryTheory.ShortComplex.RightHomologyData.opcyclesIso_inv_comp_descOpcycles · cited by 2RightHomologyData.opcycle…CategoryTheory.ShortComplex.RightHomologyData.ι_descQ_eq_zero_of_boundary · cited by 2RightHomologyData.ι_descQ…CategoryTheory.ShortComplex.isIso_opcyclesMap'_of_isIso_of_epi · cited by 1ShortComplex.isIso_opcycl…CategoryTheory.ShortComplex.RightHomologyData.ofIsLimitKernelFork_descQ · cited by 0RightHomologyData.ofIsLim…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.ShortComplex.X₂ · cited by 1115ShortComplex.X₂CategoryTheory.ShortComplex.X₁ · cited by 889ShortComplex.X₁CategoryTheory.ShortComplex.f · cited by 653ShortComplex.fCategoryTheory.ShortComplex.RightHomologyData · cited by 211ShortComplex.RightHomolog…CategoryTheory.ShortComplex.RightHomologyData.Q · cited by 163RightHomologyData.QCategoryTheory.ShortComplex.RightHomologyData.p · cited by 84RightHomologyData.pCategoryTheory.Limits.IsColimit.fac · cited by 82IsColimit.facCategoryTheory.Limits.CokernelCofork.ofπ · cited by 77CokernelCofork.ofπCategoryTheory.ShortComplex.RightHomologyData.descQ · cited by 11RightHomologyData.descQCategoryTheory.ShortComplex.RightHomologyData.hp · cited by 5RightHomologyData.hpRightHomologyData.p_descQCITED BYCITES

Cites15

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Cited by8

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