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### 11 Meet-semilattice of multiple differences

#### 11.1 Constructors

##### 11.1-1 MeetSemilatticeOfMultipleDifferences
 ‣ MeetSemilatticeOfMultipleDifferences( L ) ( attribute )

Returns: a CAP category

Construct the meet-semilattice of multiple differences from the lattice L.

##### 11.1-2 AsMultipleDifference
 ‣ AsMultipleDifference( D1, D2, ... ) ( function )

Returns: an object in a CAP category

If D1=$$A1-B1$$, D2=$$A2-B2$$, ..., then the output is DirectProduct$$(A1,A2,...)$$ - Coproduct$$(B1,B2,...)$$.

#### 11.2 Attributes

##### 11.2-1 AsSingleDifference
 ‣ AsSingleDifference( A ) ( attribute )

#### 11.3 Operations

##### 11.3-1 ListOfSingleDifferences
 ‣ ListOfSingleDifferences( A ) ( operation )

Returns: a list of CAP morphism

A list of formal single differences in the underlying lattice representing the formal multiple difference A.

##### 11.3-2 
 ‣ ( arg1, arg2 ) ( operation )

#### 11.4 GAP categories

##### 11.4-1 IsMeetSemilatticeOfMultipleDifferences
 ‣ IsMeetSemilatticeOfMultipleDifferences( arg ) ( filter )

Returns: true or false

The GAP category of a meet-semilattice of multiple differences.

##### 11.4-2 IsObjectInMeetSemilatticeOfMultipleDifferences
 ‣ IsObjectInMeetSemilatticeOfMultipleDifferences( object ) ( filter )

Returns: true or false

The GAP category of objects in a meet-semilattice of multiple differences.

##### 11.4-3 IsMorphismInMeetSemilatticeOfMultipleDifferences
 ‣ IsMorphismInMeetSemilatticeOfMultipleDifferences( morphism ) ( filter )

Returns: true or false

The GAP category of morphisms in a meet-semilattice of multiple differences.

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