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Theorems · Theorem · category theory

CategoryTheory.Abelian.Ext.ext

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C]
  [inst_2 : CategoryTheory.HasExt C] {X Y : C} [inst_3 : HasDerivedCategory C] {n : ℕ}
  {α β : CategoryTheory.Abelian.Ext X Y n}, α.hom = β.hom → α = β
Defined in
Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic
Cited by
31 results in Mathlib
Foundations
Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExtHasDerivedCategory

Around this declaration

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

CategoryTheory.Abelian.Ext.mk₀_comp_mk₀ · cited by 10Ext.mk₀_comp_mk₀CategoryTheory.Abelian.Ext.zero_comp · cited by 10Ext.zero_compCategoryTheory.Abelian.Ext.mk₀_zero · cited by 7Ext.mk₀_zeroCategoryTheory.Abelian.Ext.comp_zero · cited by 7Ext.comp_zeroCategoryTheory.Abelian.Ext.mk₀_id_comp · cited by 5Ext.mk₀_id_compCategoryTheory.Abelian.Ext.comp_mk₀_id · cited by 5Ext.comp_mk₀_idCategoryTheory.Abelian.Ext.add_hom · cited by 4Ext.add_homCategoryTheory.Abelian.Ext.mk₀_smul · cited by 3Ext.mk₀_smulCategoryTheory.Abelian.Ext.mapExactFunctor_extClass · cited by 2Ext.mapExactFunctor_extCl…CategoryTheory.Abelian.Ext.comp_add · cited by 2Ext.comp_addCategoryTheory.Abelian.Ext.comp_smul · cited by 2Ext.comp_smulCategoryTheory.Abelian.Ext.smul_comp · cited by 2Ext.smul_compCategoryTheory.Abelian.Ext.ext_iff · cited by 1Ext.ext_iffCategoryTheory.InjectiveResolution.extEquivCohomologyClass_symm_add · cited by 1InjectiveResolution.extEq…CategoryTheory.ProjectiveResolution.extEquivCohomologyClass_symm_add · cited by 1ProjectiveResolution.extE…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianEquiv.injective · cited by 464Equiv.injectiveCategoryTheory.HasExt · cited by 218CategoryTheory.HasExtCategoryTheory.Abelian.Ext · cited by 191Abelian.ExtHasDerivedCategory · cited by 190HasDerivedCategoryDerivedCategory · cited by 165DerivedCategoryCategoryTheory.ShiftedHom · cited by 88CategoryTheory.ShiftedHomDerivedCategory.singleFunctor · cited by 78DerivedCategory.singleFun…CategoryTheory.Abelian.Ext.hom · cited by 42Ext.homCategoryTheory.Abelian.Ext.homEquiv · cited by 8Ext.homEquivExt.extCITED BYCITES

Cites12

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Cited by31

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