Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Ind

### 6 Topos operations

#### 6.1 Double-pushout rewriting

We compute the double-pushout rewriting of a quiver $$G$$, given rewriting span $$l, r$$ and the matching $$m: L \rightarrow G$$:

gap> L := CreateQuiver( 3, [ 1,0,  2,0,  2,2 ] );
<An object in FinQuivers>
gap> R := CreateQuiver( 4, [ 0,1,  2,0,  0,3 ] );
<An object in FinQuivers>
gap> l := Subobject( L, [ 0, 1 ], [ ] );
<A monomorphism in FinQuivers>
gap> r := Subobject( R, [ 0, 1 ], [ ] );
<A monomorphism in FinQuivers>
gap> G := CreateQuiver( 4, [ 1,0,  3,0,  3,3,  2,0,  2,1 ] );
<An object in FinQuivers>
gap> m := Subobject( G, [ 3, 1, 2 ] );
<A monomorphism in FinQuivers>
gap> Source( m ) = L;
true
gap> p := DPO( m, l, r );;
gap> p[2];
<A monomorphism in FinQuivers>
gap> Display( p[2] );
Image of <(V)>:
{ 0,..., 3 } ⱶ[ 0, 2, 3, 4 ]→ { 0,..., 4 }

Image of <(A)>:
{ 0, 1, 2 } ⱶ[ 2, 3, 4 ]→ { 0,..., 4 }

A morphism in FinQuivers
given by the above data

Goto Chapter: Top 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Ind

generated by GAPDoc2HTML