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9 Tools
 9.1 Tools for quivers
 9.2 Tools for categories

9 Tools

9.1 Tools for quivers

9.1-1 DefiningPairOfAQuiver
‣ DefiningPairOfAQuiver( q )( attribute )

Returns: a pair

Return a pair consisting of the number of vertices 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> DefiningPairOfAQuiver( q );
[ 5, [ [ 0, 0 ], [ 0, 1 ], [ 0, 1 ], [ 3, 0 ] ] ]

9.1-2 DefiningPairOfUnderlyingQuiver
‣ DefiningPairOfUnderlyingQuiver( C )( attribute )

Returns: a pair

The defining pair of the quiver underlying the finitely presented category C.

9.2 Tools for categories

9.2-1 NerveTruncatedInDegree2Data
‣ NerveTruncatedInDegree2Data( C )( attribute )

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

The nerve data of the category C.

9.2-2 DataTablesOfCategory
‣ DataTablesOfCategory( C )( attribute )

Returns: a pair of lists

The data tables of the category C.

9.2-3 OppositeFiniteCategory
‣ OppositeFiniteCategory( C )( attribute )

Returns: a CAP category

The opposite category of a finite category C.

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