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11 Meet-semilattice of multiple differences
 11.1 Constructors
 11.2 Attributes
 11.3 Operations
 11.4 GAP categories

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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