Theorems · Definition · category theory

HomologicalComplex.restriction

{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' → (e : c.Embedding c') → [e.IsRelIff] → HomologicalComplex C c

Given K : HomologicalComplex C c' and e : c.Embedding c' (satisfying [e.IsRelIff]), this is the homological complex in HomologicalComplex C c obtained by restriction.

Defined in

Mathlib.Algebra.Homology.Embedding.Restriction

Cited by

88 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsComplexShape.Embedding.IsRelIff