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2 Category of relations
2.1 GAP categories
2.1-1 IsCategoryOfRelations
‣ IsCategoryOfRelations( arg ) | ( filter ) |
Returns: true or false
The GAP category of a category of relations
2.1-2 IsObjectInCategoryOfRelations
‣ IsObjectInCategoryOfRelations( arg ) | ( filter ) |
Returns: true or false
The GAP category of objects in a category of relations.
2.1-3 IsMorphismInCategoryOfRelations
‣ IsMorphismInCategoryOfRelations( arg ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a category of relations.
2.2 Constructors
2.2-1 CategoryOfRelations
‣ CategoryOfRelations( arg ) | ( attribute ) |
2.2-2 AsMorphismInCategoryOfRelations
‣ AsMorphismInCategoryOfRelations( arg ) | ( attribute ) |
2.3 Attributes
2.3-1 UnderlyingCategory
‣ UnderlyingCategory( arg ) | ( attribute ) |
2.3-2 UnitObjectInCategoryOfRelations
‣ UnitObjectInCategoryOfRelations( arg ) | ( attribute ) |
2.3-3 UnderlyingCell
‣ UnderlyingCell( arg ) | ( attribute ) |
2.3-4 UnderlyingSpan
‣ UnderlyingSpan( arg ) | ( attribute ) |
2.3-5 MaximalRelationIntoTerminalObject
‣ MaximalRelationIntoTerminalObject( arg ) | ( attribute ) |
2.3-6 PseudoInverse
‣ PseudoInverse( arg ) | ( attribute ) |
2.3-7 PseudoInverseOfHonestMorphism
‣ PseudoInverseOfHonestMorphism( arg ) | ( attribute ) |
2.3-8 EmbeddingOfRelationInDirectProduct
‣ EmbeddingOfRelationInDirectProduct( arg ) | ( attribute ) |
2.3-9 SourceProjection
‣ SourceProjection( arg ) | ( attribute ) |
2.3-10 RangeProjection
‣ RangeProjection( arg ) | ( attribute ) |
2.3-11 StandardizedSpan
‣ StandardizedSpan( arg ) | ( attribute ) |
2.3-12 MorphismByStandardizedSpan
‣ MorphismByStandardizedSpan( arg ) | ( attribute ) |
2.3-13 HonestRepresentative
‣ HonestRepresentative( arg ) | ( attribute ) |
2.4 Properties
2.4-1 IsHonest
‣ IsHonest( rho ) | ( property ) |
Returns: true or false
The input is a morphsm \(\rho\) in the category of relations. The output is true if the domain of \(\rho\) is an isomorphism.