Theorems · Definition · category theory

ComplexShape.Embedding.extendHomotopyFunctor

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

Given an embedding e : c.Embedding c' of complex shapes, this is the functor HomotopyCategory C c ⥤ HomotopyCategory C c' which extend complexes along e.

Defined in

Mathlib.Algebra.Homology.Embedding.ExtendHomotopy

Cited by

1 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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