Theorems · Definition · category theory

ComplexShape.Embedding.truncGEFunctor

{ι : Type u_1} →
  {ι' : Type u_2} →
    {c : ComplexShape ι} →
      {c' : ComplexShape ι'} →
        (e : c.Embedding c') →
          [e.IsTruncGE] →
            (C : Type u_4) →
              [inst : CategoryTheory.Category.{v_2, u_4} C] →
                [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
                  [CategoryTheory.Limits.HasZeroObject C] →
                    [CategoryTheory.CategoryWithHomology C] →
                      CategoryTheory.Functor (HomologicalComplex C c') (HomologicalComplex C c')

Given an embedding e : Embedding c c' of complex shapes which satisfy e.IsTruncGE, this is the (canonical) truncation functor HomologicalComplex C c' ⥤ HomologicalComplex C c'.

Defined in

Mathlib.Algebra.Homology.Embedding.TruncGE

Cited by

4 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ComplexShape.Embedding.IsTruncGECategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectCategoryTheory.CategoryWithHomology