Theorems · Definition · category theory

CategoryTheory.ShortComplex.isoCyclesOfIsLimit

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      (S : CategoryTheory.ShortComplex C) →
        [inst_2 : S.HasLeftHomology] →
          {kf : CategoryTheory.Limits.KernelFork S.g} → CategoryTheory.Limits.IsLimit kf → (kf.pt ≅ S.cycles)

The isomorphism from the point of a limit kernel fork of S.g to S.cycles.

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

11 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomology