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Theorems · Definition · category theory

CategoryTheory.Functor.shift

{C : Type u_1} →
  {A : Type u_3} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_3, u_3} A] →
        (F : CategoryTheory.Functor C A) →
          {M : Type u_4} →
            [inst_2 : AddMonoid M] →
              [inst_3 : CategoryTheory.HasShift C M] → [F.ShiftSequence M] → M → CategoryTheory.Functor C A

The shifted functors given by the shift sequence.

Defined in
Mathlib.CategoryTheory.Shift.ShiftSequence
Cited by
85 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.CategoryAddMonoidCategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequence

Around this declaration

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

CategoryTheory.Functor.shiftIso · cited by 36Functor.shiftIsoCategoryTheory.Functor.shiftMap · cited by 24Functor.shiftMapCategoryTheory.Functor.homologySequenceδ · cited by 23Functor.homologySequenceδCategoryTheory.Functor.homologySequence_exact₂ · cited by 8Functor.homologySequence_…CategoryTheory.Functor.comp_homologySequenceδ · cited by 6Functor.comp_homologySequ…CategoryTheory.Functor.ShiftSequence.induced · cited by 6ShiftSequence.inducedCategoryTheory.Functor.isoShift · cited by 6Functor.isoShiftCategoryTheory.Functor.homologySequence_comp · cited by 6Functor.homologySequence_…CategoryTheory.Functor.homologySequence_exact₃ · cited by 6Functor.homologySequence_…CategoryTheory.Functor.homologySequence_exact₁ · cited by 5Functor.homologySequence_…CategoryTheory.Functor.homologySequenceδ_comp · cited by 5Functor.homologySequenceδ…CategoryTheory.Functor.shiftMap_comp · cited by 4Functor.shiftMap_compCategoryTheory.Functor.shiftMap_comp' · cited by 4Functor.shiftMap_comp'CategoryTheory.Functor.isoShiftZero · cited by 4Functor.isoShiftZeroCochainComplex.homologyFunctorFactors_hom_app_homologyδOfTriangle · cited by 4CochainComplex.homologyFu…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorAddMonoid · cited by 2864AddMonoidCategoryTheory.HasShift · cited by 1527CategoryTheory.HasShiftCategoryTheory.Functor.ShiftSequence · cited by 61Functor.ShiftSequenceCategoryTheory.Functor.ShiftSequence.sequence · cited by 3ShiftSequence.sequenceFunctor.shiftCITED BYCITES

Cites6

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Cited by95

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