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 AThe shifted functors given by the shift sequence.
- Cited by
- 85 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- CategoryTheory.Functorstatement and proof · cited by 16,252
- AddMonoidstatement and proof · cited by 2,864
- CategoryTheory.HasShiftstatement and proof · cited by 1,527
- CategoryTheory.Functor.ShiftSequencestatement and proof · cited by 61
- CategoryTheory.Functor.ShiftSequence.sequenceproof · cited by 3
Cited by95
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.shiftIsostatement · cited by 36
- CategoryTheory.Functor.shiftMapstatement and proof · cited by 24
- CategoryTheory.Functor.homologySequenceδstatement · cited by 23
- CategoryTheory.Functor.homologySequence_exact₂statement and proof · cited by 8
- CategoryTheory.Functor.comp_homologySequenceδstatement and proof · cited by 6
- CategoryTheory.Functor.ShiftSequence.inducedstatement and proof · cited by 6
- CategoryTheory.Functor.isoShiftstatement · cited by 6
- CategoryTheory.Functor.homologySequence_compstatement and proof · cited by 6
- CategoryTheory.Functor.homologySequence_exact₃statement and proof · cited by 6
- CategoryTheory.Functor.homologySequence_exact₁statement and proof · cited by 5
- CategoryTheory.Functor.homologySequenceδ_compstatement and proof · cited by 5
- CategoryTheory.Functor.shiftMap_compstatement and proof · cited by 4