Theorems · Definition · category theory

HomologicalComplex.extendMap

{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 L : HomologicalComplex C c} → (K ⟶ L) → (e : c.Embedding c') → K.extend e ⟶ L.extend e

Given an embedding e : c.Embedding c' of complexes shapes, this is the morphism K.extend e ⟶ L.extend e induced by a morphism K ⟶ L in HomologicalComplex C c.

Defined in

Mathlib.Algebra.Homology.Embedding.Extend

Cited by

27 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms