OAI/Algebra/Finitistic/Bar/ResolutionDerived.lean
7 declarations, 0 contain sorry, 0 declared as axioms
- lemma
OAI.DerivedBar.resolution_map_isIsoline 15 - def
OAI.DerivedBar.resolutionLiftUpline 19Source 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 …
- def
OAI.DerivedBar.resolutionLiftline 28Source documentation
Full faithfulness of precomposition by the localization descends that map.
def resolutionLift (G : E ⥤ H) (β : L ⋙ G ⟶ F) : G ⟶ LF := …
- lemma
OAI.DerivedBar.whisker_resolutionLiftline 32 - lemma
OAI.DerivedBar.resolutionLift_facline 38 - lemma
OAI.DerivedBar.resolutionLift_uniqueline 50 - theorem
OAI.DerivedBar.isLeftDerivedFunctor_of_resolutionline 70Source 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 …