Theorems · Inductive type · category theory

CategoryTheory.Functor.PreservesLeftHomologyOf

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
          [inst_3 : CategoryTheory.Limits.HasZeroMorphisms D] →
            (F : CategoryTheory.Functor C D) → [F.PreservesZeroMorphisms] → CategoryTheory.ShortComplex C → Prop

A functor preserves the left homology of a short complex S if it preserves all the left homology data of S.

Defined in

Mathlib.Algebra.Homology.ShortComplex.PreservesHomology

Cited by

35 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphisms