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11 Tools

11.1 Attributes

11.1-1 Dimension
 ‣ Dimension( C ) ( attribute )

Returns: an integer

Return the dimension of the object-finite linear category C with free external Homs of finite rank.

11.2 Tools for quivers

11.2-1 DefiningTripleOfAQuiver
 ‣ DefiningTripleOfAQuiver( q ) ( attribute )

Returns: a triple

Return a triple consisting of the number of vertices of the quiver q, the number of arrows of the quiver q, and a list of pairs of integers encoding the arrows of q.

gap> LoadPackage( "Algebroids" );
true
gap> q := RightQuiver( "q(0..4)[a:0->0,s:0->1,t:0->1,m:3->0]" );
q(0,1,2,3,4)[a:0->0,s:0->1,t:0->1,m:3->0]
gap> DefiningTripleOfAQuiver( q );
[ 5, 4, [ [ 0, 0 ], [ 0, 1 ], [ 0, 1 ], [ 3, 0 ] ] ]


11.3 Tools for categories

11.3-1 NerveTruncatedInDegree2Data
 ‣ NerveTruncatedInDegree2Data( C ) ( attribute )

Returns: a pair consisting of a triple and an 8-tuple

The nerve data of the category C.

11.3-2 IndicesOfGeneratingMorphismsFromHomStructure
 ‣ IndicesOfGeneratingMorphismsFromHomStructure( C ) ( attribute )

Returns: a list of integers

The normalized indices of the generating morphisms of the finite category C.

11.3-3 OppositeFiniteCategory
 ‣ OppositeFiniteCategory( C ) ( attribute )

Returns: a CAP category

The opposite category of a finite category C.

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