Theorems · Definition · category theory

ComplexShape.Embedding.extendHomotopyFunctorFactors

{ι : Type u_1} →
  {ι' : Type u_2} →
    {c : ComplexShape ι} →
      {c' : ComplexShape ι'} →
        (e : c.Embedding c') →
          [inst : e.IsRelIff] →
            (C : Type u_3) →
              [inst_1 : CategoryTheory.Category.{v_1, u_3} C] →
                [inst_2 : CategoryTheory.Limits.HasZeroObject C] →
                  [inst_3 : CategoryTheory.Preadditive C] →
                    (HomotopyCategory.quotient C c).comp (e.extendHomotopyFunctor C) ≅
                      (e.extendFunctor C).comp (HomotopyCategory.quotient C c')

Given an embedding e : c.Embedding c' of complex shapes, the functor e.extendHomotopyFunctor C on homotopy categories is induced by the functor e.extendFunctor C on homological complexes.

Defined in

Mathlib.Algebra.Homology.Embedding.ExtendHomotopy

Cited by

1 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ComplexShape.Embedding.IsRelIffCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Preadditive