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9 Meet-semilattice of single/multiple differences
 9.1 Properties
 9.2 Attributes
 9.3 Operations
 9.4 GAP categories

9 Meet-semilattice of single/multiple differences

9.1 Properties

9.1-1 IsClosed
‣ IsClosed( A )( operation )

The embedding of the meet-semilattice of formal single/multiple differences into the underlying lattice has a right adjoint, at least in case the underying lattice is a co-Heyting algebra. A formal single difference is closed if its component of the unit of the above adjunction is an isomorphism.

9.1-2 IsOpen
‣ IsOpen( A )( property )

Returns: true or false

Check if the complement (a constructible object) of A is closed.

9.1-3 IsLocallyClosed
‣ IsLocallyClosed( A )( property )

Returns: true or false

9.2 Attributes

9.2-1 UnderlyingCategory
‣ UnderlyingCategory( D )( attribute )

Returns: a CAP category

The category underlying the meet-semilattice of single/multiple differences D.

9.2-2 LocallyClosedPart
‣ LocallyClosedPart( A )( attribute )

9.2-3 CanonicalObject
‣ CanonicalObject( A )( attribute )

9.2-4 FactorizeObject
‣ FactorizeObject( A )( attribute )

9.2-5 Closure
‣ Closure( A )( attribute )

Returns: an object in a co-Heyting algebra.

The closure of the formal single difference A in the underlying co-Heyting algebra.

9.2-6 Dimension
‣ Dimension( A )( attribute )

9.3 Operations

9.3-1 NormalizeObject
‣ NormalizeObject( A )( operation )

9.3-2 StandardizeObject
‣ StandardizeObject( A )( operation )

9.4 GAP categories

9.4-1 IsMeetSemilatticeOfDifferences
‣ IsMeetSemilatticeOfDifferences( object )( filter )

Returns: true or false

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

9.4-2 IsObjectInMeetSemilatticeOfDifferences
‣ IsObjectInMeetSemilatticeOfDifferences( object )( filter )

Returns: true or false

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

9.4-3 IsMorphismInMeetSemilatticeOfDifferences
‣ IsMorphismInMeetSemilatticeOfDifferences( morphism )( filter )

Returns: true or false

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

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