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Theorems · Theorem · category theory

CategoryTheory.ShortComplex.ShortExact.extClass_hom

∀ {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)
  [inst_3 : HasDerivedCategory C], hS.extClass.hom = hS.singleδ
Defined in
Mathlib.Algebra.Homology.DerivedCategory.Ext.ExtClass
Cited by
6 results in Mathlib
Foundations
Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.HasExtHasDerivedCategory
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Around this declaration

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

CategoryTheory.Abelian.Ext.preadditiveCoyoneda_homologySequenceδ_singleTriangle_apply · cited by 2Ext.preadditiveCoyoneda_h…CategoryTheory.Abelian.Ext.preadditiveYoneda_homologySequenceδ_singleTriangle_apply · cited by 2Ext.preadditiveYoneda_hom…CategoryTheory.Abelian.Ext.mapExactFunctor_extClass · cited by 2Ext.mapExactFunctor_extCl…CategoryTheory.ShortComplex.ShortExact.extClass_comp · cited by 1ShortExact.extClass_compCategoryTheory.ShortComplex.ShortExact.comp_extClass · cited by 1ShortExact.comp_extClassCategoryTheory.ShortComplex.ShortExact.extClass_naturality · cited by 0ShortExact.extClass_natur…DFunLike.coe · cited by 62936DFunLike.coeCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.Category.id_comp · cited by 1998Category.id_compCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.Abelian · cited by 1753CategoryTheory.AbelianShortExact.extClass_homCITED BYCITES

Cites59

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Cited by6

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