Theorems · Definition · category theory

HomologicalComplex.stupidTruncXIso

{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') →
                    [inst_3 : e.IsRelIff] → {i : ι} → {i' : ι'} → e.f i = i' → ((K.stupidTrunc e).X i' ≅ K.X i')

The isomorphism (K.stupidTrunc e).X i' ≅ K.X i' when i is in the image of e.f.

Defined in

Mathlib.Algebra.Homology.Embedding.StupidTrunc

Cited by

4 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectComplexShape.Embedding.IsRelIff