diff --git a/LeanCondensed/Mathlib/CategoryTheory/Sites/DirectImage.lean b/LeanCondensed/Mathlib/CategoryTheory/Sites/DirectImage.lean index 88707a3..bf98552 100644 --- a/LeanCondensed/Mathlib/CategoryTheory/Sites/DirectImage.lean +++ b/LeanCondensed/Mathlib/CategoryTheory/Sites/DirectImage.lean @@ -28,7 +28,7 @@ def inverseDirectImageAdjunction : ((F.op.lanAdjunction A).comp (sheafificationAdjunction K A)).restrictFullyFaithful (fullyFaithfulSheafToPresheaf J A) (Functor.FullyFaithful.id _) (Iso.refl _) (Iso.refl _) -@[simp, reassoc] +@[simp] lemma inverseDirectImageAdjunction_unit_app_val (X : Sheaf J A) : ((inverseDirectImageAdjunction J K A F).unit.app X).val = F.op.lanUnit.app X.val ≫ whiskerLeft F.op (toSheafify K (F.op.lan.obj X.val)) := by @@ -40,7 +40,6 @@ lemma inverseDirectImageAdjunction_unit_app_val (X : Sheaf J A) : Functor.associator_inv_app, Category.comp_id, Iso.refl_hom, NatTrans.id_app, Functor.comp_map, Functor.map_id, whiskerLeft_id'] -@[simp, reassoc] lemma inverseDirectImageAdjunction_unit_app_val_app (X : Sheaf J A) (Y : C) : ((inverseDirectImageAdjunction J K A F).unit.app X).val.app ⟨Y⟩ = (F.op.lanUnit.app X.val).app ⟨Y⟩ ≫ (toSheafify K (F.op.lan.obj X.val)).app ⟨F.obj Y⟩ := by @@ -48,7 +47,7 @@ lemma inverseDirectImageAdjunction_unit_app_val_app (X : Sheaf J A) (Y : C) : inverseDirectImageAdjunction_unit_app_val, whiskeringLeft_obj_obj, NatTrans.comp_app, Functor.op_obj, whiskerLeft_app] -@[simp, reassoc] +@[simp] lemma inverseDirectImageAdjunction_counit_app (X : Sheaf K A) : ((inverseDirectImageAdjunction J K A F).counit.app X) = (presheafToSheaf K A).map ((F.op.lanAdjunction A).counit.app X.val) ≫ @@ -72,14 +71,10 @@ def equivPresheafUnderlying : PUnitᵒᵖ ⥤ A ≌ A where unitIso := by refine NatIso.ofComponents (fun X ↦ NatIso.ofComponents (fun ⟨⟨⟩⟩ ↦ Iso.refl _) ?_) ?_ · intro ⟨⟨⟩⟩ ⟨⟨⟩⟩ _ - simp only [Functor.id_obj, Functor.comp_obj, Functor.const_obj_obj, Iso.refl_hom, - Category.comp_id, Functor.const_obj_map] - simp only [← Functor.map_id] - congr + simp [← Functor.map_id] + rfl · aesop counitIso := Iso.refl _ - functor_unitIso_comp := by simp only [Functor.id_obj, Functor.comp_obj, Functor.const_obj_obj, - NatIso.ofComponents_hom_app, Iso.refl_hom, NatTrans.id_app, Category.comp_id, implies_true] def equivSheafPresheaf : Sheaf pointTopology A ≌ PUnitᵒᵖ ⥤ A where functor := sheafToPresheaf _ _