Theorems · Definition · category theory

CategoryTheory.ShortComplex.HomologyData.ofAbelian

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Abelian C] → (S : CategoryTheory.ShortComplex C) → S.HomologyData

The canonical HomologyData of a short complex S in an abelian category.

Defined in: Mathlib.Algebra.Homology.ShortComplex.Abelian
Cited by: 0 results in Mathlib
Foundations: Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

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CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.CategoryStruct.compproof · cited by 17,999
CategoryTheory.ShortComplexstatement and proof · cited by 1,850
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.ShortComplex.gproof · cited by 658
CategoryTheory.ShortComplex.fproof · cited by 653
CategoryTheory.Limits.kernel.ιproof · cited by 214
CategoryTheory.Limits.cokernel.πproof · cited by 194
CategoryTheory.ShortComplex.HomologyDatastatement · cited by 102
CategoryTheory.ShortComplex.RightHomologyData.ofAbelianproof · cited by 4
CategoryTheory.ShortComplex.LeftHomologyData.ofAbelianproof · cited by 4
CategoryTheory.Abelian.coimageIsoImageproof · cited by 3

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