[MathJax off]
3 Modules over internal algebras
3.1 Constructors
3.1-1 InternalModule
‣ InternalModule( alpha, AMod ) | ( operation ) |
Returns: a CAP category object in filter IsInternalModule
3.1-2 FreeInternalModule
‣ FreeInternalModule( U, AMod ) | ( operation ) |
‣ FreeInternalModule( U, degree, AMod ) | ( operation ) |
3.1-3 InternalModuleMorphism
‣ InternalModuleMorphism( M, phi, N ) | ( operation ) |
Returns: a CAP category morphism in filter IsInternalModuleMorphism
3.2 Operations
3.2-1 FreeInternalModuleActionMorphism
‣ FreeInternalModuleActionMorphism( U, SVmod ) | ( operation ) |
‣ FreeInternalModuleActionMorphism( U, degree, SVmod ) | ( operation ) |
Returns: a morphism in a positively Z-graded category
3.2-2 UniversalMorphismFromFreeModule
‣ UniversalMorphismFromFreeModule( phi, M ) | ( operation ) |
‣ UniversalMorphismFromFreeModule( M, chi, degree, i ) | ( operation ) |
‣ UniversalMorphismFromFreeModule( M, chi, i ) | ( operation ) |
‣ UniversalMorphismFromFreeModule( M, degree ) | ( operation ) |
Returns: a CAP morphism
3.2-3 []
‣ []( c, n ) | ( operation ) |
Returns: a CAP category
The i-th degree part of the cell (=object or morphism) c.
3.2-4 Sublist
‣ Sublist( c, L ) | ( operation ) |
Returns: a CAP category
The L-th sublist of the cell (=object or morphism) c.
3.2-5 IsWellDefined
‣ IsWellDefined( cell, degree ) | ( operation ) |
‣ IsWellDefined( cell, L ) | ( operation ) |
Returns: true or a list
3.3 GAP Categories
3.3-1 IsCategoryOfInternalModules
‣ IsCategoryOfInternalModules( arg ) | ( filter ) |
Returns: true or false
3.3-2 IsCategoryOfInternalLeftModules
‣ IsCategoryOfInternalLeftModules( arg ) | ( filter ) |
Returns: true or false
3.3-3 IsCategoryOfInternalRightModules
‣ IsCategoryOfInternalRightModules( arg ) | ( filter ) |
Returns: true or false
3.3-4 IsInternalModuleCell
‣ IsInternalModuleCell( arg ) | ( filter ) |
Returns: true or false
3.3-5 IsInternalModule
‣ IsInternalModule( arg ) | ( filter ) |
Returns: true or false
3.3-6 IsInternalLeftModule
‣ IsInternalLeftModule( arg ) | ( filter ) |
Returns: true or false
3.3-7 IsInternalRightModule
‣ IsInternalRightModule( arg ) | ( filter ) |
Returns: true or false
3.3-8 IsInternalModuleMorphism
‣ IsInternalModuleMorphism( arg ) | ( filter ) |
Returns: true or false
3.3-9 IsInternalLeftModuleMorphism
‣ IsInternalLeftModuleMorphism( arg ) | ( filter ) |
Returns: true or false
3.3-10 IsInternalRightModuleMorphism
‣ IsInternalRightModuleMorphism( arg ) | ( filter ) |
Returns: true or false