Theorems · Definition · category theory

HomologicalComplex.truncLEMap

{ι : Type u_1} →
  {ι' : Type u_2} →
    {c : ComplexShape ι} →
      {c' : ComplexShape ι'} →
        {C : Type u_3} →
          [inst : CategoryTheory.Category.{v_1, u_3} C] →
            [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
              {K L : HomologicalComplex C c'} →
                (K ⟶ L) →
                  (e : c.Embedding c') →
                    [inst_2 : e.IsTruncLE] →
                      [inst_3 : ∀ (i' : ι'), K.HasHomology i'] →
                        [inst_4 : ∀ (i' : ι'), L.HasHomology i'] →
                          [inst_5 : CategoryTheory.Limits.HasZeroObject C] → K.truncLE e ⟶ L.truncLE e

The morphism K.truncLE e ⟶ L.truncLE e induced by a morphism K ⟶ L.

Defined in

Mathlib.Algebra.Homology.Embedding.TruncLE

Cited by

7 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsComplexShape.Embedding.IsTruncLEHomologicalComplex.HasHomologyHomologicalComplex.HasHomologyCategoryTheory.Limits.HasZeroObject