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1. class Functor f => Monoidal (f :: Type -> Type)

   invertible	Control.Invertible.Monoidal

   Invariant monoidal functor. This roughly corresponds to Applicative, which, for covariant functors, is equivalent to a monoidal functor. Invariant functors, however, may admit a monoidal instance but not applicative.

2. class Monoidal f => MonoidalAlt (f :: Type -> Type)

   invertible	Control.Invertible.Monoidal

   Monoidal functors that allow choice.

3. module Data.Bifunctor.Monoidal

   No documentation available.

4. class (Tensor cat t1 i1, Tensor cat t2 i2, Tensor cat to io, Semigroupal cat t1 t2 to f, Unital cat i1 i2 io f) => Monoidal (cat :: Type -> Type -> Type) (t1 :: Type -> Type -> Type) i1 (t2 :: Type -> Type -> Type) i2 (to :: Type -> Type -> Type) io (f :: Type -> Type -> Type)

   monoidal-functors	Data.Bifunctor.Monoidal

   Given monoidal categories <math> and <math>. A bifunctor <math> is Monoidal if it maps between <math> and <math> while preserving their monoidal structure. Eg., a homomorphism of monoidal categories. See NCatlab for more details.

   Laws

   Right Unitality: <math>

   combine . grmap introduce ≡ bwd unitr . fwd unitr
   

   Left Unitality: <math>

   combine . glmap introduce ≡ fmap (bwd unitl) . fwd unitl
   

5. module Data.Functor.Monoidal

   No documentation available.

6. class (Tensor cat t1 i1, Tensor cat t0 i0, Semigroupal cat t1 t0 f, Unital cat i1 i0 f) => Monoidal (cat :: Type -> Type -> Type) (t1 :: Type -> Type -> Type) i1 (t0 :: Type -> Type -> Type) i0 (f :: Type -> Type)

   monoidal-functors	Data.Functor.Monoidal

   Given monoidal categories <math> and <math>. A functor <math> is Monoidal if it maps between <math> and <math> while preserving their monoidal structure. Eg., a homomorphism of monoidal categories. See NCatlab for more details.

   Laws

   Right Unitality: <math>

   combine . grmap introduce ≡ bwd unitr . fwd unitr
   

   Left Unitality: <math>

   combine . glmap introduce ≡ fmap (bwd unitl) . fwd unitl
   

7. module Data.Trifunctor.Monoidal

   No documentation available.

8. class (Tensor cat t1 i1, Tensor cat t2 i2, Tensor cat t3 i3, Tensor cat to io, Semigroupal cat t1 t2 t3 to f, Unital cat i1 i2 i3 io f) => Monoidal (cat :: Type -> Type -> Type) (t1 :: Type -> Type -> Type) i1 (t2 :: Type -> Type -> Type) i2 (t3 :: Type -> Type -> Type) i3 (to :: Type -> Type -> Type) io (f :: Type -> Type -> Type -> Type)

   monoidal-functors	Data.Trifunctor.Monoidal

   Given monoidal categories <math> and <math>. A bifunctor <math> is Monoidal if it maps between <math> and <math> while preserving their monoidal structure. Eg., a homomorphism of monoidal categories. See NCatlab for more details.

   Laws

   Right Unitality: <math>

   combine . grmap introduce ≡ bwd unitr . fwd unitr
   

   Left Unitality: <math>

   combine . glmap introduce ≡ fmap (bwd unitl) . fwd unitl
   

9. class (LeftModule Natural m, RightModule Natural m) => Monoidal m

   algebra	Numeric.Algebra

   An additive monoid

   zero + a = a = a + zero
   

10. class (LeftModule Natural m, RightModule Natural m) => Monoidal m

    algebra	Numeric.Algebra.Class

    An additive monoid

    zero + a = a = a + zero
    

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