Theorems · Definition · category theory

ComplexShape.Embedding.extendFunctor

{ι : Type u_1} →
  {ι' : Type u_2} →
    {c : ComplexShape ι} →
      {c' : ComplexShape ι'} →
        c.Embedding c' →
          (C : Type u_3) →
            [inst : CategoryTheory.Category.{v_1, u_3} C] →
              [CategoryTheory.Limits.HasZeroObject C] →
                [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
                  CategoryTheory.Functor (HomologicalComplex C c) (HomologicalComplex C c')

Given an embedding e : c.Embedding c' of complex shapes, this is the functor HomologicalComplex C c ⥤ HomologicalComplex C c' which extend complexes along e: the extended complexes are zero in the degrees that are not in the image of e.f.

Defined in

Mathlib.Algebra.Homology.Embedding.Extend

Cited by

5 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphisms