Theorems · Definition · category theory

CategoryTheory.ShortComplex.leftHomologyFunctor

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      [CategoryTheory.Limits.HasKernels C] →
        [CategoryTheory.Limits.HasCokernels C] → CategoryTheory.Functor (CategoryTheory.ShortComplex C) C

The left homology functor ShortComplex C ⥤ C, where the left homology of a short complex S is understood as a cokernel of the obvious map S.toCycles : S.X₁ ⟶ S.cycles where S.cycles is a kernel of S.g : S.X₂ ⟶ S.X₃.

Defined in

Mathlib.Algebra.Homology.ShortComplex.LeftHomology

Cited by

7 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasKernelsCategoryTheory.Limits.HasCokernels