OAI/Algebra/Finitistic/Bar/CountRetracts.lean

GitHub source file

9 declarations, 0 contain sorry, 0 declared as axioms

  1. def OAI.DerivedBar.directSumComplexProjection line 12

    Source documentation

    Projection from the original chain direct sum to its r-th complex.

    def directSumComplexProjection (S : ℕ → ChainComplex (ModuleCat.{u} D) ℕ) (r : ℕ) :
        directSumComplex S ⟶ S r where
    …

    Mentions: OAI.DerivedBar.directSumComplex

  2. theorem OAI.DerivedBar.directSumComplex_inclusion_projection line 25
  3. theorem OAI.DerivedBar.ParityBridge.mapped_retract line 36
  4. def OAI.DerivedBar.ParityBridge.countTensorBarInclusion line 64

    Source documentation

    The original count subcomplex included into the actual balanced tensor bar.

    def countTensorBarInclusion (r : ℕ) : S r ⟶ T :=
    …
  5. def OAI.DerivedBar.ParityBridge.countTensorBarProjection line 68
  6. theorem OAI.DerivedBar.ParityBridge.countTensorBar_retract line 72
  7. def OAI.DerivedBar.ParityBridge.shiftedIterateInclusion line 78

    Source documentation

    The genuine shifted iterate included into actual left-derived base change.

    def shiftedIterateInclusion (r : ℕ) :
        (shiftedIterateDiagram k D X N).obj ⟨r⟩ ⟶
          (derivedBaseChange D (fstHom k D X)).obj (ModuleCat.of A N) :=
    …

    Mentions: OAI.DerivedBar.ParityBridge.shiftedIterateDiagram, OAI.DerivedBar.derivedBaseChange

  8. def OAI.DerivedBar.ParityBridge.shiftedIterateProjection line 85
  9. theorem OAI.DerivedBar.ParityBridge.shiftedIterate_retract line 92