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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.

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