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Theorems · Theorem · category theory

CategoryTheory.ShortComplex.ShortExact.extClass_comp

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.HasExt C] {S : CategoryTheory.ShortComplex C} (hS : S.ShortExact),
  hS.extClass.comp (CategoryTheory.Abelian.Ext.mk₀ S.f) ⋯ = 0
Defined in
Mathlib.Algebra.Homology.DerivedCategory.Ext.ExtClass
Cited by
1 results in Mathlib
Foundations
Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExt
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Around this declaration

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CategoryTheory.ShortComplex.ShortExact.extClass_comp_assoc · cited by 0ShortExact.extClass_comp_…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.map · cited by 8698Functor.mapadd_zero · cited by 2707add_zeroCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianCategoryTheory.ShortComplex.X₂ · cited by 1115ShortComplex.X₂CategoryTheory.ShortComplex.X₁ · cited by 889ShortComplex.X₁CategoryTheory.ShortComplex.X₃ · cited by 876ShortComplex.X₃CategoryTheory.ShortComplex.f · cited by 653ShortComplex.fCategoryTheory.ShortComplex.ShortExact · cited by 232ShortComplex.ShortExactCategoryTheory.HasExt · cited by 218CategoryTheory.HasExtCategoryTheory.Abelian.Ext · cited by 191Abelian.ExtHasDerivedCategory · cited by 190HasDerivedCategoryCategoryTheory.Abelian.Ext.mk₀ · cited by 94Ext.mk₀CategoryTheory.Abelian.Ext.comp · cited by 80Ext.compShortExact.extClass_compCITED BYCITES

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Cited by1

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