Theorems · Inductive type · category theory

HomologicalComplex.IsSupportedOutside

{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] → HomologicalComplex C c' → c.Embedding c' → Prop

If K : HomologicalComplex C c', then K.IsSupportedOutside e holds for an embedding e : c.Embedding c' of complex shapes if K is exact at e.f i for all i.

Defined in

Mathlib.Algebra.Homology.Embedding.IsSupported

Cited by

8 results in Mathlib

Foundations

Depth 3 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms