category_theory.monoidal.rigid.of_equivalence
⟷
Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -29,8 +29,8 @@ variable (F : MonoidalFunctor C D)
/-- Given candidate data for an exact pairing,
which is sent by a faithful monoidal functor to an exact pairing,
the equations holds automatically. -/
-def exactPairingOfFaithful [Faithful F.toFunctor] {X Y : C} (eval : Y ⊗ X ⟶ 𝟙_ C)
- (coeval : 𝟙_ C ⟶ X ⊗ Y) [ExactPairing (F.obj X) (F.obj Y)]
+def exactPairingOfFaithful [CategoryTheory.Functor.Faithful F.toFunctor] {X Y : C}
+ (eval : Y ⊗ X ⟶ 𝟙_ C) (coeval : 𝟙_ C ⟶ X ⊗ Y) [ExactPairing (F.obj X) (F.obj Y)]
(map_eval : F.map eval = inv (F.μ _ _) ≫ ε_ _ _ ≫ F.ε)
(map_coeval : F.map coeval = inv F.ε ≫ η_ _ _ ≫ F.μ _ _) : ExactPairing X Y
where
@@ -47,8 +47,9 @@ def exactPairingOfFaithful [Faithful F.toFunctor] {X Y : C} (eval : Y ⊗ X ⟶
/-- Given a pair of objects which are sent by a fully faithful functor to a pair of objects
with an exact pairing, we get an exact pairing.
-/
-def exactPairingOfFullyFaithful [Full F.toFunctor] [Faithful F.toFunctor] (X Y : C)
- [ExactPairing (F.obj X) (F.obj Y)] : ExactPairing X Y :=
+def exactPairingOfFullyFaithful [CategoryTheory.Functor.Full F.toFunctor]
+ [CategoryTheory.Functor.Faithful F.toFunctor] (X Y : C) [ExactPairing (F.obj X) (F.obj Y)] :
+ ExactPairing X Y :=
exactPairingOfFaithful F (F.toFunctor.preimage (inv (F.μ _ _) ≫ ε_ _ _ ≫ F.ε))
(F.toFunctor.preimage (inv F.ε ≫ η_ _ _ ≫ F.μ _ _)) (by simp) (by simp)
#align category_theory.exact_pairing_of_fully_faithful CategoryTheory.exactPairingOfFullyFaithful
@@ -57,8 +58,9 @@ def exactPairingOfFullyFaithful [Full F.toFunctor] [Faithful F.toFunctor] (X Y :
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
#print CategoryTheory.hasLeftDualOfEquivalence /-
/-- Pull back a left dual along an equivalence. -/
-def hasLeftDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasLeftDual (F.obj X)] :
- HasLeftDual X where
+def hasLeftDualOfEquivalence [CategoryTheory.Functor.IsEquivalence F.toFunctor] (X : C)
+ [HasLeftDual (F.obj X)] : HasLeftDual X
+ where
leftDual := F.toFunctor.inv.obj (ᘁF.obj X)
exact := by
apply exact_pairing_of_fully_faithful F _ _
@@ -71,8 +73,9 @@ def hasLeftDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasLeftDual (F
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
#print CategoryTheory.hasRightDualOfEquivalence /-
/-- Pull back a right dual along an equivalence. -/
-def hasRightDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasRightDual (F.obj X)] :
- HasRightDual X where
+def hasRightDualOfEquivalence [CategoryTheory.Functor.IsEquivalence F.toFunctor] (X : C)
+ [HasRightDual (F.obj X)] : HasRightDual X
+ where
rightDual := F.toFunctor.inv.obj (F.obj Xᘁ)
exact := by
apply exact_pairing_of_fully_faithful F _ _
@@ -84,21 +87,22 @@ def hasRightDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasRightDual
#print CategoryTheory.leftRigidCategoryOfEquivalence /-
/-- Pull back a left rigid structure along an equivalence. -/
-def leftRigidCategoryOfEquivalence [IsEquivalence F.toFunctor] [LeftRigidCategory D] :
- LeftRigidCategory C where leftDual X := hasLeftDualOfEquivalence F X
+def leftRigidCategoryOfEquivalence [CategoryTheory.Functor.IsEquivalence F.toFunctor]
+ [LeftRigidCategory D] : LeftRigidCategory C where leftDual X := hasLeftDualOfEquivalence F X
#align category_theory.left_rigid_category_of_equivalence CategoryTheory.leftRigidCategoryOfEquivalence
-/
#print CategoryTheory.rightRigidCategoryOfEquivalence /-
/-- Pull back a right rigid structure along an equivalence. -/
-def rightRigidCategoryOfEquivalence [IsEquivalence F.toFunctor] [RightRigidCategory D] :
- RightRigidCategory C where rightDual X := hasRightDualOfEquivalence F X
+def rightRigidCategoryOfEquivalence [CategoryTheory.Functor.IsEquivalence F.toFunctor]
+ [RightRigidCategory D] : RightRigidCategory C where rightDual X := hasRightDualOfEquivalence F X
#align category_theory.right_rigid_category_of_equivalence CategoryTheory.rightRigidCategoryOfEquivalence
-/
#print CategoryTheory.rigidCategoryOfEquivalence /-
/-- Pull back a rigid structure along an equivalence. -/
-def rigidCategoryOfEquivalence [IsEquivalence F.toFunctor] [RigidCategory D] : RigidCategory C
+def rigidCategoryOfEquivalence [CategoryTheory.Functor.IsEquivalence F.toFunctor]
+ [RigidCategory D] : RigidCategory C
where
leftDual X := hasLeftDualOfEquivalence F X
rightDual X := hasRightDualOfEquivalence F X
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.CategoryTheory.Monoidal.Rigid.Basic
+import CategoryTheory.Monoidal.Rigid.Basic
#align_import category_theory.monoidal.rigid.of_equivalence from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.monoidal.rigid.of_equivalence
-! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Monoidal.Rigid.Basic
+#align_import category_theory.monoidal.rigid.of_equivalence from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
/-!
# Transport rigid structures over a monoidal equivalence.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -28,6 +28,7 @@ variable (F : MonoidalFunctor C D)
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.exactPairingOfFaithful /-
/-- Given candidate data for an exact pairing,
which is sent by a faithful monoidal functor to an exact pairing,
the equations holds automatically. -/
@@ -43,7 +44,9 @@ def exactPairingOfFaithful [Faithful F.toFunctor] {X Y : C} (eval : Y ⊗ X ⟶
coevaluation_evaluation' :=
F.toFunctor.map_injective (by simp [map_eval, map_coeval, monoidal_functor.map_tensor])
#align category_theory.exact_pairing_of_faithful CategoryTheory.exactPairingOfFaithful
+-/
+#print CategoryTheory.exactPairingOfFullyFaithful /-
/-- Given a pair of objects which are sent by a fully faithful functor to a pair of objects
with an exact pairing, we get an exact pairing.
-/
@@ -52,8 +55,10 @@ def exactPairingOfFullyFaithful [Full F.toFunctor] [Faithful F.toFunctor] (X Y :
exactPairingOfFaithful F (F.toFunctor.preimage (inv (F.μ _ _) ≫ ε_ _ _ ≫ F.ε))
(F.toFunctor.preimage (inv F.ε ≫ η_ _ _ ≫ F.μ _ _)) (by simp) (by simp)
#align category_theory.exact_pairing_of_fully_faithful CategoryTheory.exactPairingOfFullyFaithful
+-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.hasLeftDualOfEquivalence /-
/-- Pull back a left dual along an equivalence. -/
def hasLeftDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasLeftDual (F.obj X)] :
HasLeftDual X where
@@ -64,8 +69,10 @@ def hasLeftDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasLeftDual (F
dsimp
infer_instance
#align category_theory.has_left_dual_of_equivalence CategoryTheory.hasLeftDualOfEquivalence
+-/
/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print CategoryTheory.hasRightDualOfEquivalence /-
/-- Pull back a right dual along an equivalence. -/
def hasRightDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasRightDual (F.obj X)] :
HasRightDual X where
@@ -76,6 +83,7 @@ def hasRightDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasRightDual
dsimp
infer_instance
#align category_theory.has_right_dual_of_equivalence CategoryTheory.hasRightDualOfEquivalence
+-/
#print CategoryTheory.leftRigidCategoryOfEquivalence /-
/-- Pull back a left rigid structure along an equivalence. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
! This file was ported from Lean 3 source module category_theory.monoidal.rigid.of_equivalence
-! leanprover-community/mathlib commit a6275694804455fe8995bd530e86b67ddab5cff1
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -12,6 +12,9 @@ import Mathbin.CategoryTheory.Monoidal.Rigid.Basic
/-!
# Transport rigid structures over a monoidal equivalence.
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725
@@ -74,22 +74,28 @@ def hasRightDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasRightDual
infer_instance
#align category_theory.has_right_dual_of_equivalence CategoryTheory.hasRightDualOfEquivalence
+#print CategoryTheory.leftRigidCategoryOfEquivalence /-
/-- Pull back a left rigid structure along an equivalence. -/
def leftRigidCategoryOfEquivalence [IsEquivalence F.toFunctor] [LeftRigidCategory D] :
LeftRigidCategory C where leftDual X := hasLeftDualOfEquivalence F X
#align category_theory.left_rigid_category_of_equivalence CategoryTheory.leftRigidCategoryOfEquivalence
+-/
+#print CategoryTheory.rightRigidCategoryOfEquivalence /-
/-- Pull back a right rigid structure along an equivalence. -/
def rightRigidCategoryOfEquivalence [IsEquivalence F.toFunctor] [RightRigidCategory D] :
RightRigidCategory C where rightDual X := hasRightDualOfEquivalence F X
#align category_theory.right_rigid_category_of_equivalence CategoryTheory.rightRigidCategoryOfEquivalence
+-/
+#print CategoryTheory.rigidCategoryOfEquivalence /-
/-- Pull back a rigid structure along an equivalence. -/
def rigidCategoryOfEquivalence [IsEquivalence F.toFunctor] [RigidCategory D] : RigidCategory C
where
leftDual X := hasLeftDualOfEquivalence F X
rightDual X := hasRightDualOfEquivalence F X
#align category_theory.rigid_category_of_equivalence CategoryTheory.rigidCategoryOfEquivalence
+-/
end CategoryTheory
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
These notions on functors are now Functor.Full
, Functor.Faithful
, Functor.EssSurj
, Functor.IsEquivalence
, Functor.ReflectsIsomorphisms
. Deprecated aliases are introduced for the previous names.
@@ -24,7 +24,7 @@ variable (F : MonoidalFunctor C D)
/-- Given candidate data for an exact pairing,
which is sent by a faithful monoidal functor to an exact pairing,
the equations holds automatically. -/
-def exactPairingOfFaithful [Faithful F.toFunctor] {X Y : C} (eval : Y ⊗ X ⟶ 𝟙_ C)
+def exactPairingOfFaithful [F.Faithful] {X Y : C} (eval : Y ⊗ X ⟶ 𝟙_ C)
(coeval : 𝟙_ C ⟶ X ⊗ Y) [ExactPairing (F.obj X) (F.obj Y)]
(map_eval : F.map eval = inv (F.μ _ _) ≫ ε_ _ _ ≫ F.ε)
(map_coeval : F.map coeval = inv F.ε ≫ η_ _ _ ≫ F.μ _ _) : ExactPairing X Y where
@@ -43,14 +43,14 @@ def exactPairingOfFaithful [Faithful F.toFunctor] {X Y : C} (eval : Y ⊗ X ⟶
/-- Given a pair of objects which are sent by a fully faithful functor to a pair of objects
with an exact pairing, we get an exact pairing.
-/
-def exactPairingOfFullyFaithful [Full F.toFunctor] [Faithful F.toFunctor] (X Y : C)
+def exactPairingOfFullyFaithful [F.Full] [F.Faithful] (X Y : C)
[ExactPairing (F.obj X) (F.obj Y)] : ExactPairing X Y :=
exactPairingOfFaithful F (F.toFunctor.preimage (inv (F.μ _ _) ≫ ε_ _ _ ≫ F.ε))
(F.toFunctor.preimage (inv F.ε ≫ η_ _ _ ≫ F.μ _ _)) (by simp) (by simp)
#align category_theory.exact_pairing_of_fully_faithful CategoryTheory.exactPairingOfFullyFaithful
/-- Pull back a left dual along an equivalence. -/
-def hasLeftDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasLeftDual (F.obj X)] :
+def hasLeftDualOfEquivalence [F.IsEquivalence] (X : C) [HasLeftDual (F.obj X)] :
HasLeftDual X where
leftDual := F.toFunctor.inv.obj (ᘁ(F.obj X))
exact := by
@@ -63,7 +63,7 @@ def hasLeftDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasLeftDual (F
#align category_theory.has_left_dual_of_equivalence CategoryTheory.hasLeftDualOfEquivalence
/-- Pull back a right dual along an equivalence. -/
-def hasRightDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasRightDual (F.obj X)] :
+def hasRightDualOfEquivalence [F.IsEquivalence] (X : C) [HasRightDual (F.obj X)] :
HasRightDual X where
rightDual := F.toFunctor.inv.obj ((F.obj X)ᘁ)
exact := by
@@ -74,17 +74,17 @@ def hasRightDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasRightDual
#align category_theory.has_right_dual_of_equivalence CategoryTheory.hasRightDualOfEquivalence
/-- Pull back a left rigid structure along an equivalence. -/
-def leftRigidCategoryOfEquivalence [IsEquivalence F.toFunctor] [LeftRigidCategory D] :
+def leftRigidCategoryOfEquivalence [F.IsEquivalence] [LeftRigidCategory D] :
LeftRigidCategory C where leftDual X := hasLeftDualOfEquivalence F X
#align category_theory.left_rigid_category_of_equivalence CategoryTheory.leftRigidCategoryOfEquivalence
/-- Pull back a right rigid structure along an equivalence. -/
-def rightRigidCategoryOfEquivalence [IsEquivalence F.toFunctor] [RightRigidCategory D] :
+def rightRigidCategoryOfEquivalence [F.IsEquivalence] [RightRigidCategory D] :
RightRigidCategory C where rightDual X := hasRightDualOfEquivalence F X
#align category_theory.right_rigid_category_of_equivalence CategoryTheory.rightRigidCategoryOfEquivalence
/-- Pull back a rigid structure along an equivalence. -/
-def rigidCategoryOfEquivalence [IsEquivalence F.toFunctor] [RigidCategory D] : RigidCategory C where
+def rigidCategoryOfEquivalence [F.IsEquivalence] [RigidCategory D] : RigidCategory C where
leftDual X := hasLeftDualOfEquivalence F X
rightDual X := hasRightDualOfEquivalence F X
#align category_theory.rigid_category_of_equivalence CategoryTheory.rigidCategoryOfEquivalence
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -19,7 +19,6 @@ namespace CategoryTheory
open MonoidalCategory
variable {C D : Type*} [Category C] [Category D] [MonoidalCategory C] [MonoidalCategory D]
-
variable (F : MonoidalFunctor C D)
/-- Given candidate data for an exact pairing,
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -55,7 +55,7 @@ def hasLeftDualOfEquivalence [IsEquivalence F.toFunctor] (X : C) [HasLeftDual (F
HasLeftDual X where
leftDual := F.toFunctor.inv.obj (ᘁ(F.obj X))
exact := by
- -- porting note: in Lean3, `apply exactPairingOfFullyFaithful F _ _` automatically
+ -- Porting note: in Lean3, `apply exactPairingOfFullyFaithful F _ _` automatically
-- created the goals for `ExactPairing` type class
refine @exactPairingOfFullyFaithful _ _ _ _ _ _ F _ _ _ _ ?_
refine @exactPairingCongrLeft _ _ _ _ _ _ ?_ (F.toFunctor.asEquivalence.counitIso.app _)
@@ -22,8 +22,6 @@ variable {C D : Type*} [Category C] [Category D] [MonoidalCategory C] [MonoidalC
variable (F : MonoidalFunctor C D)
-attribute [local simp] id_tensorHom tensorHom_id
-
/-- Given candidate data for an exact pairing,
which is sent by a faithful monoidal functor to an exact pairing,
the equations holds automatically. -/
@@ -36,11 +34,11 @@ def exactPairingOfFaithful [Faithful F.toFunctor] {X Y : C} (eval : Y ⊗ X ⟶
evaluation_coevaluation' :=
F.toFunctor.map_injective <| by
simp [map_eval, map_coeval,
- MonoidalFunctor.map_whiskerLeft', MonoidalFunctor.map_whiskerRight']
+ MonoidalFunctor.map_whiskerLeft, MonoidalFunctor.map_whiskerRight]
coevaluation_evaluation' :=
F.toFunctor.map_injective <| by
simp [map_eval, map_coeval,
- MonoidalFunctor.map_whiskerLeft', MonoidalFunctor.map_whiskerRight']
+ MonoidalFunctor.map_whiskerLeft, MonoidalFunctor.map_whiskerRight]
#align category_theory.exact_pairing_of_faithful CategoryTheory.exactPairingOfFaithful
/-- Given a pair of objects which are sent by a fully faithful functor to a pair of objects
@@ -22,6 +22,8 @@ variable {C D : Type*} [Category C] [Category D] [MonoidalCategory C] [MonoidalC
variable (F : MonoidalFunctor C D)
+attribute [local simp] id_tensorHom tensorHom_id
+
/-- Given candidate data for an exact pairing,
which is sent by a faithful monoidal functor to an exact pairing,
the equations holds automatically. -/
@@ -32,9 +34,13 @@ def exactPairingOfFaithful [Faithful F.toFunctor] {X Y : C} (eval : Y ⊗ X ⟶
evaluation' := eval
coevaluation' := coeval
evaluation_coevaluation' :=
- F.toFunctor.map_injective (by simp [map_eval, map_coeval, MonoidalFunctor.map_tensor])
+ F.toFunctor.map_injective <| by
+ simp [map_eval, map_coeval,
+ MonoidalFunctor.map_whiskerLeft', MonoidalFunctor.map_whiskerRight']
coevaluation_evaluation' :=
- F.toFunctor.map_injective (by simp [map_eval, map_coeval, MonoidalFunctor.map_tensor])
+ F.toFunctor.map_injective <| by
+ simp [map_eval, map_coeval,
+ MonoidalFunctor.map_whiskerLeft', MonoidalFunctor.map_whiskerRight']
#align category_theory.exact_pairing_of_faithful CategoryTheory.exactPairingOfFaithful
/-- Given a pair of objects which are sent by a fully faithful functor to a pair of objects
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -18,7 +18,7 @@ namespace CategoryTheory
open MonoidalCategory
-variable {C D : Type _} [Category C] [Category D] [MonoidalCategory C] [MonoidalCategory D]
+variable {C D : Type*} [Category C] [Category D] [MonoidalCategory C] [MonoidalCategory D]
variable (F : MonoidalFunctor C D)
@@ -2,14 +2,11 @@
Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.monoidal.rigid.of_equivalence
-! leanprover-community/mathlib commit a6275694804455fe8995bd530e86b67ddab5cff1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Monoidal.Rigid.Basic
+#align_import category_theory.monoidal.rigid.of_equivalence from "leanprover-community/mathlib"@"a6275694804455fe8995bd530e86b67ddab5cff1"
+
/-!
# Transport rigid structures over a monoidal equivalence.
-/
@@ -19,6 +19,8 @@ noncomputable section
namespace CategoryTheory
+open MonoidalCategory
+
variable {C D : Type _} [Category C] [Category D] [MonoidalCategory C] [MonoidalCategory D]
variable (F : MonoidalFunctor C D)