Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

Complexes as Presheaves #156

Merged
merged 1 commit into from
Jun 21, 2023
Merged

Complexes as Presheaves #156

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
2 changes: 1 addition & 1 deletion Bicomplexes/PackageInfo.g
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -11,7 +11,7 @@ SetPackageInfo( rec(

PackageName := "Bicomplexes",
Subtitle := "Bicomplexes for Abelian categories",
Version := "2023.05-02",
Version := "2023.06-01",
Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ),
License := "GPL-2.0-or-later",

Expand Down
26 changes: 10 additions & 16 deletions Bicomplexes/gap/Bicomplexes.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -68,21 +68,19 @@ BindGlobal( "CREATE_BICOMPLEXES_CATEGORY",
coch_cat := UnderlyingCategory( modeling_cat );

objects := AsZFunction(
i -> ObjectConstructor( coch_cat,
[ AsZFunction( j -> datum[1](i, j) ),
i -> CreateComplex( coch_cat,
AsZFunction( j -> datum[1](i, j) ),
AsZFunction( j -> (-1)^i * datum[3](i, j) ),
datum[6],
datum[7] ] ) );
datum[7] ) );

diffs := AsZFunction(
i -> MorphismConstructor( coch_cat,
i -> CreateComplexMorphism( coch_cat,
objects[i],
[ AsZFunction( j -> datum[2]( i, j ) ),
datum[6],
datum[7] ],
AsZFunction( j -> datum[2]( i, j ) ),
objects[i+index_shift] ) );

return ObjectConstructor( modeling_cat, [ objects, diffs, datum[4], datum[5] ] );
return CreateComplex( modeling_cat, objects, diffs, datum[4], datum[5] );

end;

Expand All @@ -107,18 +105,14 @@ BindGlobal( "CREATE_BICOMPLEXES_CATEGORY",
coch_cat := UnderlyingCategory( modeling_cat );

morphisms := AsZFunction(
i -> MorphismConstructor( coch_cat,
i -> CreateComplexMorphism( coch_cat,
source[i],
[ AsZFunction( j -> datum( i, j ) ),
Minimum( LowerBound( source[i] ), LowerBound( range[i] ) ),
Maximum( UpperBound( source[i] ), UpperBound( range[i] ) ) ],
AsZFunction( j -> datum( i, j ) ),
range[i] ) );

return MorphismConstructor( modeling_cat,
return CreateComplexMorphism( modeling_cat,
source,
[ morphisms,
Minimum( LowerBound( source ), LowerBound( range ) ),
Maximum( UpperBound( source ), UpperBound( range ) ) ],
morphisms,
range );

end;
Expand Down
2 changes: 1 addition & 1 deletion Bicomplexes/gap/TotalComplex.gi
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -55,7 +55,7 @@ BindGlobal( "TOTAL_COMPLEX_OF_BICOMPLEX",
objs[index+sign]
) );

return ObjectConstructor( complexes_cat, [ objs, diffs, l+b, r+a ] );
return CreateComplex( complexes_cat, objs, diffs, l+b, r+a );

end );

Expand Down
17 changes: 6 additions & 11 deletions Bicomplexes/tst/total-complex-of-bicomplex-morphism-using-algebroids.tst
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -136,13 +136,12 @@ gap> rels := [ PreCompose( dA1_m2, dA1_m1 ),
> -PreCompose( f4_m1, dB4_m1 ) + PreCompose( dA4_m1, f4_0 ),
> -PreCompose( f4_0, dB4_0 ) + PreCompose( dA4_0, f4_1 ),
> -PreCompose( f4_1, dB4_1 ) + PreCompose( dA4_1, f4_2) ];;
gap> oid := kF / rels;;
gap> oid := AlgebroidFromDataTables( kF / rels );;
gap> Aoid := AdditiveClosure( oid );;
gap> cochains_Aoid := ComplexesCategoryByCochains( Aoid );;
gap> cochains_cochains_Aoid := ComplexesCategoryByCochains( cochains_Aoid );;
gap> cochains_bicomplexes_Aoid := BicomplexesCategoryByCochains( Aoid );;
gap> IsIdenticalObj( cochains_cochains_Aoid, ModelingCategory( cochains_bicomplexes_Aoid ) );
true
gap> Assert( 0, IsIdenticalObj( cochains_cochains_Aoid, ModelingCategory( cochains_bicomplexes_Aoid ) ) );
gap> for object_info in objects do
> MakeReadWriteGlobal( object_info[1] );
> DeclareSynonym( object_info[1],
Expand All @@ -165,20 +164,16 @@ gap> for morphism_info in morphisms do
gap> A := CreateComplex( cochains_cochains_Aoid, [ dA_1, dA_2, dA_3 ], 1 );;
gap> B := CreateComplex( cochains_cochains_Aoid, [ dB_1, dB_2, dB_3 ], 1 );;
gap> f := CreateComplexMorphism( cochains_cochains_Aoid, A, [ f1, f2, f3, f4 ], 1, B );;
gap> ForAll( [ A, B, f ], IsWellDefined );
true
gap> Assert( 0, ForAll( [ A, B, f ], IsWellDefined ) );
gap> A := CreateBicomplex( cochains_bicomplexes_Aoid, A );;
gap> B := CreateBicomplex( cochains_bicomplexes_Aoid, B );;
gap> f := CreateBicomplexMorphism( cochains_bicomplexes_Aoid, f );;
gap> ForAll( [ A, B, f ], IsWellDefined );
true
gap> Assert( 0, ForAll( [ A, B, f ], IsWellDefined ) );
gap> total_f := TotalComplexFunctorial( TotalComplex(A), f, TotalComplex(B) );;
gap> IsWellDefined( total_f );
true
gap> Assert( 0, IsWellDefined( total_f ) );
gap> chains_bicomplexes_Aoid := BicomplexesCategoryByChains( Aoid );;
gap> A := CreateBicomplex( chains_bicomplexes_Aoid, A );;
gap> B := CreateBicomplex( chains_bicomplexes_Aoid, B );;
gap> f := CreateBicomplexMorphism( chains_bicomplexes_Aoid, f );;
gap> total_f := TotalComplexFunctorial( TotalComplex(A), f, TotalComplex(B) );;
gap> IsWellDefined( total_f );
true
gap> Assert( 0, IsWellDefined( total_f ) );
12 changes: 7 additions & 5 deletions ComplexesCategories/PackageInfo.g
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -10,7 +10,7 @@ SetPackageInfo( rec(

PackageName := "ComplexesCategories",
Subtitle := "Category of (co)chain complexes of an additive category",
Version := "2023.05-02",
Version := "2023.06-01",
Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ),
License := "GPL-2.0-or-later",

Expand Down Expand Up @@ -73,13 +73,15 @@ PackageDoc := rec(

Dependencies := rec(
GAP := ">= 4.12.1",
NeededOtherPackages := [
[ "AutoDoc", ">= 2019.09.04" ],
NeededOtherPackages := [ [ "AutoDoc", ">= 2019.09.04" ],
[ "CAP", ">= 2023.05-03" ],
[ "ToolsForHigherHomologicalAlgebra", ">= 2022.12-05" ],
[ "PreSheaves", ">= 2023.05-03" ],
],
SuggestedOtherPackages := [ ],


SuggestedOtherPackages := [ #[ "Locales", ">= 2023.05-05" ],
],

ExternalConditions := [ ],
),

Expand Down
2 changes: 1 addition & 1 deletion ComplexesCategories/examples/notebooks/FreydCategory_Qxy.ipynb
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -156,7 +156,7 @@
"text": [
"A CAP category with name Complexes category by cochains( Freyd( Rows( Q[x,y,z] ) ) ):\n",
"\n",
"79 primitive operations were used to derive 325 operations for this category which algorithmically\n",
"84 primitive operations were used to derive 327 operations for this category which algorithmically\n",
"* IsEquippedWithHomomorphismStructure\n",
"* IsLinearCategoryOverCommutativeRing\n",
"* IsAbelianCategory\n"
Expand Down
4 changes: 2 additions & 2 deletions ComplexesCategories/examples/notebooks/PreSheaves.ipynb
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -355,7 +355,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"77 primitive operations were used to derive 324 operations for this category which algorithmically\n",
"82 primitive operations were used to derive 326 operations for this category which algorithmically\n",
"* IsEquippedWithHomomorphismStructure\n",
"* IsLinearCategoryOverCommutativeRing\n",
"* IsAbelianCategory\n"
Expand Down Expand Up @@ -1044,7 +1044,7 @@
{
"data": {
"text/plain": [
"GAP: <A morphism in Complexes category by cochains( PreSheaves( Algebroid( Q, FreeCategory( RightQuiver( \"q_𝓞(𝓞₀,𝓞₁,𝓞₂)[x₀:𝓞₀->𝓞₁,x₁:𝓞₀->𝓞₁,x₂:𝓞₀->𝓞₁,y₀:𝓞₁->𝓞₂,y₁:𝓞₁->𝓞₂,y₂:𝓞₁->𝓞₂]\" ) ) ) / relations, Rows( Q ) ) ) supported on the interval [ 0 ]>"
"GAP: <A morphism in Complexes category by cochains( PreSheaves( Algebroid( Q, FreeCategory( RightQuiver( \"q_𝓞(𝓞₀,𝓞₁,𝓞₂)[x₀:𝓞₀->𝓞₁,x₁:𝓞₀->𝓞₁,x₂:𝓞₀->𝓞₁,y₀:𝓞₁->𝓞₂,y₁:𝓞₁->𝓞₂,y₂:𝓞₁->𝓞₂]\" ) ) ) / relations, Rows( Q ) ) ) supported on the interval [ 0 .. 2 ]>"
]
},
"execution_count": 32,
Expand Down
2 changes: 2 additions & 0 deletions ComplexesCategories/gap/Categories.gd
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -40,6 +40,8 @@ DeclareCategory( "IsComplexesCategoryByCochains", IsComplexesCategory );
#
###################################################

DeclareGlobalFunction( "COMPLEXES_CATEGORY_BY_COCHAINS_AS_TOWER" );

#! @Description
#! Creates the complexes category by cochains $\mathcal{C}^b(A)$ of an additive category $A$.
#! @Arguments A
Expand Down
Loading