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13 Meet-semilattice of single/multiple differences
 13.1 GAP Categories
 13.2 Properties
 13.3 Attributes
 13.4 Operations

13 Meet-semilattice of single/multiple differences

13.1 GAP Categories

13.1-1 IsMeetSemilatticeOfDifferences
‣ IsMeetSemilatticeOfDifferences( object )( filter )

Returns: true or false

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

13.1-2 IsObjectInMeetSemilatticeOfDifferences
‣ IsObjectInMeetSemilatticeOfDifferences( object )( filter )

Returns: true or false

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

13.1-3 IsMorphismInMeetSemilatticeOfDifferences
‣ IsMorphismInMeetSemilatticeOfDifferences( morphism )( filter )

Returns: true or false

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

13.2 Properties

13.2-1 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.

13.2-2 IsOpen
‣ IsOpen( A )( property )

Returns: true or false

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

13.2-3 IsLocallyClosed
‣ IsLocallyClosed( A )( property )

Returns: true or false

13.3 Attributes

13.3-1 UnderlyingCategory
‣ UnderlyingCategory( D )( attribute )

Returns: a CAP category

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

13.3-2 LocallyClosedPart
‣ LocallyClosedPart( A )( attribute )

13.3-3 CanonicalObject
‣ CanonicalObject( A )( attribute )

13.3-4 FactorizeObject
‣ FactorizeObject( A )( attribute )

13.3-5 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.

13.3-6 Dimension
‣ Dimension( A )( attribute )

13.4 Operations

13.4-1 NormalizeObject
‣ NormalizeObject( A )( operation )

13.4-2 StandardizeObject
‣ StandardizeObject( A )( operation )
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