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Theorems · Theorem · category theory

CategoryTheory.Abelian.Ext.comp_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.HasExt C] {X Y : C} {n : ℕ} (α : CategoryTheory.Abelian.Ext X Y n) (Z : C) (m p : ℕ)
  (h : n + m = p), α.comp 0 h = 0
Defined in
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic
Cited by
7 results in Mathlib
Foundations
Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExt

Around this declaration

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

CategoryTheory.Abelian.Ext.zero_hom · cited by 6Ext.zero_homCategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₃ · cited by 2ShortExact.hasProjectiveD…CategoryTheory.Retract.hasProjectiveDimensionLT · cited by 2Retract.hasProjectiveDime…CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₁ · cited by 1ShortExact.hasProjectiveD…CategoryTheory.Limits.IsZero.hasInjectiveDimensionLT_zero · cited by 1IsZero.hasInjectiveDimens…CategoryTheory.ShortComplex.ShortExact.hasProjectiveDimensionLT_X₂ · cited by 0ShortExact.hasProjectiveD…CategoryTheory.hasInjectiveDimensionLT_of_enoughProjectives · cited by 0CategoryTheory.hasInjecti…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianCategoryTheory.HasExt · cited by 218CategoryTheory.HasExtCategoryTheory.Abelian.Ext · cited by 191Abelian.ExtHasDerivedCategory · cited by 190HasDerivedCategoryCategoryTheory.Abelian.Ext.comp · cited by 80Ext.compDerivedCategory.singleFunctor · cited by 78DerivedCategory.singleFun…CategoryTheory.Abelian.Ext.hom · cited by 42Ext.homHasDerivedCategory.standard · cited by 42HasDerivedCategory.standa…CategoryTheory.ShiftedHom.comp.congr_simp · cited by 37comp.congr_simpCategoryTheory.Abelian.Ext.ext · cited by 31Ext.extCategoryTheory.Abelian.Ext.comp_hom · cited by 27Ext.comp_homCategoryTheory.ShiftedHom.comp_zero · cited by 2ShiftedHom.comp_zeroExt.comp_zeroCITED BYCITES

Cites14

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Cited by7

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