Theorems · Definition · category theory

CategoryTheory.ShortComplex.rightHomologyFunctorOpNatIso

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      [inst_2 : CategoryTheory.Limits.HasKernels C] →
        [inst_3 : CategoryTheory.Limits.HasCokernels C] →
          [inst_4 : CategoryTheory.Limits.HasKernels Cᵒᵖ] →
            [inst_5 : CategoryTheory.Limits.HasCokernels Cᵒᵖ] →
              (CategoryTheory.ShortComplex.rightHomologyFunctor C).op ≅
                (CategoryTheory.ShortComplex.opFunctor C).comp (CategoryTheory.ShortComplex.leftHomologyFunctor Cᵒᵖ)

The opposite of the right homology functor is the left homology functor.

Defined in

Mathlib.Algebra.Homology.ShortComplex.RightHomology

Cited by

2 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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