OAI/Algebra/Finitistic/Bar/ResolutionDerived.lean

GitHub source file

7 declarations, 0 contain sorry, 0 declared as axioms

  1. lemma OAI.DerivedBar.resolution_map_isIso line 15
  2. def OAI.DerivedBar.resolutionLiftUp line 19

    Source documentation

    A candidate map into the resolved model, before descending the localization.

    def resolutionLiftUp (G : E ⥤ H) (β : L ⋙ G ⟶ F) : L ⋙ G ⟶ L ⋙ LF := by
    …
  3. def OAI.DerivedBar.resolutionLift line 28

    Source documentation

    Full faithfulness of precomposition by the localization descends that map.

    def resolutionLift (G : E ⥤ H) (β : L ⋙ G ⟶ F) : G ⟶ LF :=
    …
  4. lemma OAI.DerivedBar.whisker_resolutionLift line 32
  5. lemma OAI.DerivedBar.resolutionLift_fac line 38
  6. lemma OAI.DerivedBar.resolutionLift_unique line 50
  7. theorem OAI.DerivedBar.isLeftDerivedFunctor_of_resolution line 70

    Source documentation

    A functorial resolution computes the genuine left derived functor. The criterion is a right Kan extension universal property; its hypotheses are checked on the actual bar resolution in the application.

    theorem isLeftDerivedFunctor_of_resolution : LF.IsLeftDerivedFunctor α W where
    …