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### 7 Category of algebroids

#### 7.1 Properties

##### 7.1-1 IsCommutative
 ‣ IsCommutative( A ) ( property )

Returns: true or false

Check whether the algebroid A is commutative.

##### 7.1-2 IsCounitary
 ‣ IsCounitary( B ) ( property )

Returns: true or false

Check whether B is counitary.

##### 7.1-3 IsCoassociative
 ‣ IsCoassociative( B ) ( property )

Returns: true or false

Check whether B is coassociative.

#### 7.2 Attributes

##### 7.2-1 AsCapCategory
 ‣ AsCapCategory( arg ) ( attribute )

##### 7.2-2 AsCapFunctor
 ‣ AsCapFunctor( arg ) ( attribute )

#### 7.3 Operations

##### 7.3-1 Twist
 ‣ Twist( A, B ) ( operation )

Returns: a CAP functor

Construct the canonical twist from A $$\otimes$$ B to B $$\otimes$$ A

#### 7.4 Constructors

##### 7.4-1 CategoryOfAlgebroids
 ‣ CategoryOfAlgebroids( arg1, arg2 ) ( operation )

##### 7.4-2 CategoryOfAlgebroidsObject
 ‣ CategoryOfAlgebroidsObject( arg ) ( attribute )

##### 7.4-3 CategoryOfAlgebroidsMorphism
 ‣ CategoryOfAlgebroidsMorphism( arg1, arg2, arg3 ) ( operation )

##### 7.4-4 CategoryOfAlgebroidsMorphism
 ‣ CategoryOfAlgebroidsMorphism( arg ) ( operation )

#### 7.5 GAP categories

##### 7.5-1 IsCategoryOfAlgebroidsObject
 ‣ IsCategoryOfAlgebroidsObject( object ) ( filter )

Returns: true or false

The GAP category of objects in the category of algebroids over a ring $$R$$.

##### 7.5-2 IsCategoryOfAlgebroidsMorphism
 ‣ IsCategoryOfAlgebroidsMorphism( object ) ( filter )

Returns: true or false

The GAP category of morphisms in the category of algebroids over a ring $$R$$.

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