GAP (FpCategories) - Chapter 7: Finitely presented categories generated by enhanced quivers

The full subcategory of the simplicial category \(\Delta\) on the objects \([0], \ldots, [n]\).

The full subcategory of the simplicial category \(\Delta\) on the objects \([0], [1], [2]\)

gap> LoadPackage( "Algebroids" );
true
gap> Delta2 := SimplicialCategoryTruncatedInDegree( 2 );
PathCategory( FinQuiver(
  "Delta(C0,C1,C2)[id:C1-≻C0,s:C0-≻C1,t:C0-≻C1,
                   is:C2-≻C1,it:C2-≻C1,
                   ps:C1-≻C2,pt:C1-≻C2,mu:C1-≻C2]" ) )
/ [ s⋅id = id(C0), t⋅id = id(C0), ps⋅is = id(C1), ... ]
gap> DefiningRelations( Delta2 );
[ [ s⋅id:(C0) -≻ (C0), id(C0):(C0) -≻ (C0) ],
  [ t⋅id:(C0) -≻ (C0), id(C0):(C0) -≻ (C0) ],
  [ ps⋅is:(C1) -≻ (C1), id(C1):(C1) -≻ (C1) ],
  [ pt⋅it:(C1) -≻ (C1), id(C1):(C1) -≻ (C1) ],
  [ is⋅id:(C2) -≻ (C0), it⋅id:(C2) -≻ (C0) ],
  [ pt⋅is:(C1) -≻ (C1), id⋅t:(C1) -≻ (C1) ],
  [ ps⋅it:(C1) -≻ (C1), id⋅s:(C1) -≻ (C1) ],
  [ s⋅pt:(C0) -≻ (C2), t⋅ps:(C0) -≻ (C2) ],
  [ s⋅mu:(C0) -≻ (C2), s⋅ps:(C0) -≻ (C2) ],
  [ t⋅mu:(C0) -≻ (C2), t⋅pt:(C0) -≻ (C2) ],
  [ mu⋅is:(C1) -≻ (C1), id(C1):(C1) -≻ (C1) ],
  [ mu⋅it:(C1) -≻ (C1), id(C1):(C1) -≻ (C1) ] ]
gap> Size( Delta2 );
31
gap> Delta2_op := OppositeFiniteCategory( Delta2 );
Opposite( PathCategory( FinQuiver(
  "Delta(C0,C1,C2)[id:C1-≻C0,s:C0-≻C1,t:C0-≻C1,
                   is:C2-≻C1,it:C2-≻C1,
                   ps:C1-≻C2,pt:C1-≻C2,mu:C1-≻C2]" ) ) /
[ s⋅id = id(C0), t⋅id = id(C0), ps⋅is = id(C1), ... ] )
gap> IsIdenticalObj( OppositeFiniteCategory( Delta2_op ), Delta2 );
true

7 Finitely presented categories generated by enhanced quivers

7.1 Global functions

7.1-1 SimplicialCategoryTruncatedInDegree