Theorems · Definition · category theory

CategoryTheory.ShortComplex.Exact.leftHomologyDataOfIsLimitKernelFork

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {S : CategoryTheory.ShortComplex C} →
        S.Exact →
          [CategoryTheory.Limits.HasZeroObject C] →
            (kf : CategoryTheory.Limits.KernelFork S.g) → CategoryTheory.Limits.IsLimit kf → S.LeftHomologyData

Given an exact short complex S and a limit kernel fork kf for S.g, this is the left homology data for S with K := kf.pt and H := 0.

Defined in

Mathlib.Algebra.Homology.ShortComplex.Exact

Cited by

5 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject