Theorems · Definition · category theory

HomologicalComplex.coneOfHasLimitEval

{C : Type u_1} →
  {ι : Type u_2} →
    {J : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} C] →
        [inst_1 : CategoryTheory.Category.{v_2, u_3} J] →
          {c : ComplexShape ι} →
            [inst_2 : CategoryTheory.Limits.HasZeroMorphisms C] →
              (F : CategoryTheory.Functor J (HomologicalComplex C c)) →
                [∀ (n : ι), CategoryTheory.Limits.HasLimit (F.comp (HomologicalComplex.eval C c n))] →
                  CategoryTheory.Limits.Cone F

A cone for a functor F : J ⥤ HomologicalComplex C c which is given in degree n by the limit F ⋙ eval C c n.

Defined in

Mathlib.Algebra.Homology.HomologicalComplexLimits

Cited by

3 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasLimit