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2c7d975 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | 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
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