Theorems · Definition · category theory

HomologicalComplex.extendXIso

{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.HasZeroObject C] →
              [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
                (K : HomologicalComplex C c) →
                  (e : c.Embedding c') → {i' : ι'} → {i : ι} → e.f i = i' → ((K.extend e).X i' ≅ K.X i)

The isomorphism (K.extend e).X i' ≅ K.X i when e.f i = i'.

Defined in

Mathlib.Algebra.Homology.Embedding.Extend

Cited by

56 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms