Theorems · Definition · category theory

HomologicalComplex.extend.leftHomologyData

{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] →
              [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
                (K : HomologicalComplex C c) →
                  (e : c.Embedding c') →
                    {i j k : ι} →
                      {i' j' k' : ι'} →
                        e.f j = j' →
                          c.prev j = i →
                            c'.prev j' = i' →
                              c.next j = k →
                                c'.next j' = k' →
                                  (K.sc' i j k).LeftHomologyData → ((K.extend e).sc' i' j' k').LeftHomologyData

The left homology data of (K.extend e).sc' i' j' k' that is deduced from a left homology data of K.sc' i j k.

Defined in

Mathlib.Algebra.Homology.Embedding.ExtendHomology

Cited by

5 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObject