Theorems · Definition · category theory

CategoryTheory.ShortComplex.cyclesIsKernel

{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] → CategoryTheory.Limits.IsLimit (CategoryTheory.Limits.KernelFork.ofι S.iCycles ⋯)

Via S.iCycles : S.cycles ⟶ S.X₂, the object S.cycles identifies to the kernel of S.g : S.X₂ ⟶ S.X₃.

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

5 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.ShortComplex.HasLeftHomology