openAI-math-dataset / lean /OAI /Algebra /AuslanderReiten /Resolutions /ProjectiveResolutionFunctor.lean
| import Mathlib.CategoryTheory.Abelian.Projective.Ext | |
| import Mathlib.Algebra.Homology.DerivedCategory.Ext.Map | |
| namespace OAI | |
| noncomputable section | |
| open CategoryTheory CategoryTheory.Limits HomologicalComplex | |
| namespace ArExplicit.ResolutionProducts | |
| universe u v u' v' | |
| variable {C : Type u} [Category.{v} C] [Abelian C] | |
| variable {D : Type u'} [Category.{v'} D] [Abelian D] | |
| variable (F : C ⥤ D) [F.Additive] [PreservesFiniteLimits F] [PreservesFiniteColimits F] | |
| variable [F.PreservesProjectiveObjects] | |
| variable {X : C} (P : ProjectiveResolution X) | |
| def mapResolution : ProjectiveResolution (F.obj X) where | |
| complex := (F.mapHomologicalComplex (.down ℕ)).obj P.complex | |
| projective n := F.projective_obj_of_projective (P.projective n) | |
| π := (F.mapHomologicalComplex (.down ℕ)).map P.π ≫ | |
| (singleMapHomologicalComplex F (.down ℕ) 0).hom.app X | |
| quasiIso := by infer_instance | |
| end ArExplicit.ResolutionProducts | |
| end | |
| end OAI | |