@@ -181,6 +181,8 @@ variables {D : Type u₂} [category.{v₂} D]
181
181
section
182
182
variables {F G : C ⥤ D}
183
183
184
+ local attribute [semireducible] has_hom.opposite
185
+
184
186
@[simps] protected definition op (α : F ⟶ G) : G.op ⟶ F.op :=
185
187
{ app := λ X, (α.app (unop X)).op,
186
188
naturality' := begin tidy, erw α.naturality, refl, end }
@@ -189,7 +191,14 @@ variables {F G : C ⥤ D}
189
191
190
192
@[simps] protected definition unop (α : F.op ⟶ G.op) : G ⟶ F :=
191
193
{ app := λ X, (α.app (op X)).unop,
192
- naturality' := begin tidy, erw α.naturality, refl, end }
194
+ naturality' :=
195
+ begin
196
+ intros X Y f,
197
+ have := congr_arg has_hom.hom.op (α.naturality f.op),
198
+ dsimp at this ,
199
+ erw this ,
200
+ refl,
201
+ end }
193
202
194
203
@[simp] lemma unop_id (F : C ⥤ D) : nat_trans.unop (𝟙 F.op) = 𝟙 F := rfl
195
204
198
207
section
199
208
variables {F G : C ⥤ Dᵒᵖ}
200
209
210
+ local attribute [semireducible] has_hom.opposite
211
+
201
212
protected definition left_op (α : F ⟶ G) : G.left_op ⟶ F.left_op :=
202
213
{ app := λ X, (α.app (unop X)).unop,
203
214
naturality' := begin tidy, erw α.naturality, refl, end }
208
219
209
220
protected definition right_op (α : F.left_op ⟶ G.left_op) : G ⟶ F :=
210
221
{ app := λ X, (α.app (op X)).op,
211
- naturality' := begin tidy, erw α.naturality, refl, end }
222
+ naturality' :=
223
+ begin
224
+ intros X Y f,
225
+ have := congr_arg has_hom.hom.op (α.naturality f.op),
226
+ dsimp at this ,
227
+ erw this
228
+ end }
212
229
213
230
@[simp] lemma right_op_app (α : F.left_op ⟶ G.left_op) (X) :
214
231
(nat_trans.right_op α).app X = (α.app (op X)).op :=
0 commit comments