‣ BooleanAlgebraOfConstructibleObjectsAsUnionOfMultipleDifferences( D ) | ( attribute ) |
Returns: a CAP category
Construct the Boolean algebra of constructible objects as union of objects in the poset D of multiple differences.
‣ UnionOfMultipleDifferences( 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\((B1,B2,...)\).
‣ BooleanAlgebraOfConstructibleObjectsAsUnionOfDifferences( D ) | ( attribute ) |
Returns: a CAP category
Construct the Boolean algebra of constructible objects as union of objects in the poset D of single differences.
‣ UnionOfDifferences( D1, D2, ... ) | ( function ) |
‣ UnionOfDifferencesOfNormalizedObjects( 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\((B1,B2,...)\). AsFormalDifferenceOfNormalizedMorphisms assumes that the input is normalized.
‣ IsOpen( A ) | ( property ) |
Returns: true or false
‣ IsClosed( A ) | ( operation ) |
‣ IsLocallyClosed( A ) | ( property ) |
Returns: true or false
‣ UnderlyingCategory( C ) | ( attribute ) |
Returns: a CAP category
The category underlying the Boolean algebra of constructible objects C.
‣ LocallyClosedPart( A ) | ( attribute ) |
‣ CanonicalObject( A ) | ( attribute ) |
‣ FactorizeObject( A ) | ( attribute ) |
‣ NormalizedObject( A ) | ( attribute ) |
‣ StandardizedObject( A ) | ( attribute ) |
‣ Closure( A ) | ( attribute ) |
Returns: an object in a co-Heyting algebra.
The closure of the constructible object A in the underlying co-Heyting algebra.
‣ ClosureAsConstructibleObject( A ) | ( attribute ) |
Returns: a constructible object.
The closure of the constructible object A as a constructible object.
‣ Dimension( A ) | ( attribute ) |
‣ NormalizeObject( A ) | ( operation ) |
‣ StandardizeObject( A ) | ( operation ) |
‣ Length( A ) | ( attribute ) |
12.4-4 \[\]‣ \[\]( A, i ) | ( operation ) |
‣ Iterator( A ) | ( operation ) |
‣ ForAllOp( A, f ) | ( operation ) |
‣ ForAnyOp( A, f ) | ( operation ) |
‣ ListOfObjectsInMeetSemilatticeOfMultipleDifferences( A ) | ( operation ) |
Returns: a list of CAP morphism
A list of morphisms in the underlying lattice representing the formal multiple difference A.
‣ ListOfObjectsInMeetSemilatticeOfDifferences( A ) | ( operation ) |
Returns: a list of CAP morphism
A list of morphisms in the underlying lattice representing the formal multiple difference A.
‣ IsBooleanAlgebraOfConstructibleObjects( arg ) | ( filter ) |
Returns: true or false
The GAP category of a Boolean algebra of constructible objects.
‣ IsConstructibleObject( object ) | ( filter ) |
Returns: true or false
The GAP category of objects in a Boolean algebra of constructible objects.
‣ IsMorphismBetweenConstructibleObjects( morphism ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a Boolean algebra of constructible objects.
‣ IsBooleanAlgebraOfConstructibleObjectsAsUnionOfMultipleDifferences( arg ) | ( filter ) |
Returns: true or false
The GAP category of a Boolean algebra of constructible objects as union of multiple differences.
‣ IsConstructibleObjectAsUnionOfMultipleDifferences( object ) | ( filter ) |
Returns: true or false
The GAP category of objects in ...
‣ IsMorphismBetweenConstructibleObjectsAsUnionOfMultipleDifferences( morphism ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in ...
‣ IsBooleanAlgebraOfConstructibleObjectsAsUnionOfSingleDifferences( arg ) | ( filter ) |
Returns: true or false
The GAP category of a Boolean algebra of constructible objects as union of single differences.
‣ IsConstructibleObjectAsUnionOfSingleDifferences( object ) | ( filter ) |
Returns: true or false
The GAP category of objects in a Boolean algebra of constructible objects, the latter as unions of formal single differences.
‣ IsMorphismBetweenConstructibleObjectsAsUnionOfDifferences( morphism ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a Boolean algebra of constructible objects, the latter as unions of formal single differences.
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