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Theorems · Theorem · category theory

CategoryTheory.ShortComplex.Splitting.exact

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  {S : CategoryTheory.ShortComplex C} [CategoryTheory.Limits.HasZeroObject C] (s : S.Splitting), S.Exact

A short complex equipped with a splitting is exact.

Defined in
Mathlib.Algebra.Homology.ShortComplex.Exact
Cited by
1 results in Mathlib
Foundations
Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject
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Around this declaration

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

CategoryTheory.ShortComplex.Splitting.shortExact · cited by 2Splitting.shortExactCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.ShortComplex · cited by 1850CategoryTheory.ShortCompl…CategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectCategoryTheory.ShortComplex.Exact · cited by 292ShortComplex.ExactCategoryTheory.ShortComplex.Splitting · cited by 62ShortComplex.SplittingCategoryTheory.Limits.isZero_zero · cited by 34Limits.isZero_zeroCategoryTheory.ShortComplex.Splitting.homologyData · cited by 4Splitting.homologyDataSplitting.exactCITED BYCITES

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Cited by1

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