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Theorems · Definition · category theory

HomotopyCategory.Plus.singleFunctors

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [CategoryTheory.Limits.HasZeroObject C] → CategoryTheory.SingleFunctors C (HomotopyCategory.Plus C) ℤ

The collection of all single functors C ⥤ HomotopyCategory.Plus C for n : ℤ along with their compatibilities with shifts.

Defined in
Mathlib.Algebra.Homology.HomotopyCategory.Plus
Cited by
0 results in Mathlib
Foundations
Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

HomotopyCategory.Plus.singleFunctor · cited by 0Plus.singleFunctorCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor.comp · cited by 6529Functor.compCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveCategoryTheory.Limits.HasZeroObject · cited by 1298Limits.HasZeroObjectComplexShape.up · cited by 1123ComplexShape.upCategoryTheory.Iso.refl · cited by 727Iso.reflHomotopyCategory · cited by 132HomotopyCategoryCategoryTheory.SingleFunctors · cited by 65CategoryTheory.SingleFunc…CategoryTheory.ObjectProperty.lift · cited by 33ObjectProperty.liftHomotopyCategory.plus · cited by 9HomotopyCategory.plusHomotopyCategory.Plus · cited by 8HomotopyCategory.PlusCategoryTheory.SingleFunctors.lift · cited by 5SingleFunctors.liftHomotopyCategory.singleFunctors · cited by 3HomotopyCategory.singleFu…HomotopyCategory.Plus.ι · cited by 2Plus.ιHomotopyCategory.singleFunctor · cited by 2HomotopyCategory.singleFu…Plus.singleFunctorsCITED BYCITES

Cites15

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Cited by1

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