Compute SubobjectClassifier( PreSheaves( SimplicialCategoryTruncatedInDegree( 2 ) ) )

[mohamed-barakat]

Compute SubobjectClassifier( PreSheaves( SimplicialCategoryTruncatedInDegree( 2 ) ) )

[mohamed-barakat]

Within 13h:

gap> omega := SubobjectClassifier( PreSheaves( SimplicialCategoryTruncatedInDegree( 2 ) ) );
<An object in PreSheaves( FreeCategory( RightQuiver( "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]" ) ) / relations, SkeletalFinSets )>
gap> Display( omega );
Image of <(C0)>:
{ 0, 1 }

Image of <(C1)>:
{ 0,..., 4 }

Image of <(C2)>:
{ 0,..., 18 }

Image of (C1)-[(id)]->(C0):
{ 0, 1 } ⱶ[ 0, 4 ]→ { 0,..., 4 }

Image of (C0)-[(s)]->(C1):
{ 0,..., 4 } ⱶ[ 0, 1, 0, 1, 1 ]→ { 0, 1 }

Image of (C0)-[(t)]->(C1):
{ 0,..., 4 } ⱶ[ 0, 0, 1, 1, 1 ]→ { 0, 1 }

Image of (C2)-[(is)]->(C1):
{ 0,..., 4 } ⱶ[ 0, 1, 9, 12, 18 ]→ { 0,..., 18 }

Image of (C2)-[(it)]->(C1):
{ 0,..., 4 } ⱶ[ 0, 4, 5, 11, 18 ]→ { 0,..., 18 }

Image of (C1)-[(ps)]->(C2):
{ 0,..., 18 } ⱶ[ 0, 1, 2, 3, 4, 0, 1, 1, 2, 2, 3, 4, 3, 4, 3, 4, 3, 4, 4 ]→ { 0,..., 4 }

Image of (C1)-[(pt)]->(C2):
{ 0,..., 18 } ⱶ[ 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 3, 3, 4, 4, 3, 3, 4, 4, 4 ]→ { 0,..., 4 }

Image of (C1)-[(mu)]->(C2):
{ 0,..., 18 } ⱶ[ 0, 1, 0, 1, 1, 2, 3, 4, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4 ]→ { 0,..., 4 }

An object in PreSheaves( FreeCategory( RightQuiver( "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]" ) ) / relations, Ske\
letalFinSets ) given by the above data