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### 2 Internal algebra elements

#### 2.1 Constructors

##### 2.1-1 InternalElement
 ‣ InternalElement( iota ) ( operation )
 ‣ InternalElement( A, chi, degree, i ) ( operation )
 ‣ InternalElement( A, chi, i ) ( operation )
 ‣ InternalElement( phi, M ) ( operation )
 ‣ InternalElement( M, chi, degree, i ) ( operation )
 ‣ InternalElement( M, chi, i ) ( operation )

Returns: a CAP morphism

#### 2.2 Attributes

##### 2.2-1 UnderlyingEmbedding
 ‣ UnderlyingEmbedding( p ) ( attribute )

Returns: a CAP category morphism (IsMorphismInZGradedClosureCategoryWithBounds)

##### 2.2-2 NonZeroDegrees
 ‣ NonZeroDegrees( e ) ( attribute )

Returns: a list

##### 2.2-3 NonZeroParts
 ‣ NonZeroParts( e ) ( attribute )

Returns: a list

##### 2.2-4 NonZeroPartsWithDegrees
 ‣ NonZeroPartsWithDegrees( e ) ( attribute )

Returns: a list

##### 2.2-5 SupportWithDegrees
 ‣ SupportWithDegrees( e ) ( attribute )

Returns: a list

##### 2.2-6 AdditiveInverse
 ‣ AdditiveInverse( e ) ( attribute )

Returns: an element of an internal algebra or module

##### 2.2-7 UniversalMorphismFromFreeModule
 ‣ UniversalMorphismFromFreeModule( e ) ( attribute )

Returns: a CAP morphism

#### 2.3 Operations

##### 2.3-1 InternalPreAddition
 ‣ InternalPreAddition( e1, e2 ) ( operation )

Returns: a morphism in a positively Z-graded category

##### 2.3-2 +
 ‣ +( e1, e2 ) ( operation )

Returns: an element of an internal algebra or module

##### 2.3-3 -
 ‣ -( e1, e2 ) ( operation )

Returns: an element of an internal algebra or module

##### 2.3-4 InternalPreMultiplication
 ‣ InternalPreMultiplication( a, m ) ( operation )

Returns: a morphism in a positively Z-graded category

##### 2.3-5 *
 ‣ *( a, m ) ( operation )

Returns: a ring element and an element of an internal algebra or module

##### 2.3-6 BraidedMultiplication
 ‣ BraidedMultiplication( a, b ) ( operation )

Returns: an element of an internal algebra

##### 2.3-7 []
 ‣ []( e ) ( operation )

Returns: an element of an internal algebra or module

#### 2.4 GAP Categories

##### 2.4-1 IsInternalAlgebra
 ‣ IsInternalAlgebra( arg ) ( filter )

Returns: true or false

##### 2.4-2 IsElementInInternalAlgebraOrModule
 ‣ IsElementInInternalAlgebraOrModule( arg ) ( filter )

Returns: true or false

##### 2.4-3 IsElementInInternalAlgebra
 ‣ IsElementInInternalAlgebra( arg ) ( filter )

Returns: true or false

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