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Theorems · Theorem · category theory

CategoryTheory.ShortComplex.ShortExact.comp_extClass

∀ {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),
  (CategoryTheory.Abelian.Ext.mk₀ S.g).comp hS.extClass ⋯ = 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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CategoryTheory.ShortComplex.ShortExact.comp_extClass_assoc · cited by 0ShortExact.comp_extClass_…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.map · cited by 8698Functor.mapzero_add · cited by 2366zero_addCategoryTheory.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.g · cited by 658ShortComplex.gCategoryTheory.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.comp_extClassCITED BYCITES

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