sage.categories.category

Module category_types

Specific categorie classes. This is paced in a seperate file from categories.py to avoid circular imports (as morphisms must be very low in the hierarchy with the new coercion model).

Classes

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Category_uniq

Elements
The category of all elements of a given object.

Sequences
The category of all elements of a given object.

Category_over_base

Category_over_base_ring

AbelianCategory

Category_in_ambient

Category_module

Category_ideal

Objects
The category of all SAGE objects.

Sets
The category of sets.

PointedSets
The category of pointed sets.

SetsWithPartialMaps
The category whose objects are sets and whose morphisms are maps that are allowed to raise a ValueError on some inputs.

GSets
The category of $G$-sets, for a group $G$.

Semigroups
The category of all semigroups.

Monoids
The category of monoids.

Groupoid
The category of groupoids, for a set (usually a group) $G$.

Groups
The category of groups.

AbelianSemigroups
The category of all abelian semigroups.

AbelianMonoids
The category of all monoids.

AbelianGroups
The category of all abelian groups.

Rings
The category of all rings.

CommutativeRings
The category of commutative rings.

Fields
The category of fields.

FiniteFields
The category of all finite fields.

NumberFields
The category of number fields.

Algebras
The category of algebras over a fixed base ring.

CommutativeAlgebras
The category of commutative algebras over a given base ring.

MonoidAlgebras
The category of all monoid algebras over a given base ring.

GroupAlgebras
EXAMPLES:...

MatrixAlgebras
The category of matrix algebras over a field.

RingModules
The category of all modules over a base ring.

Modules
The category of all modules over a base ring.

FreeModules
The category of free modules over a base ring.

VectorSpaces
The category of vector spaces over a specified field, with an emedding in an ambient vector space.

HeckeModules
The category of Hecke modules.

RingIdeals
The category of all ideals in a fixed ring.

Ideals
The category of all ideals in a fixed ring.

CommutativeRingIdeals
The category of ideals in a fixed commutative ring.

AlgebraModules
The category of modules over a fixed algebra $A$.

AlgebraIdeals
The category of ideals in a fixed algebra $A$.

CommutativeAlgebraIdeals
The category of ideals in a fixed commutative algebra $A$.

Schemes_over_base
The category of schemes over a given base scheme.

Schemes_abstract
The category of all abstract schemes.

ModularAbelianVarieties
The category of modular abelian varieties over a given field.

k
The category of all abelian groups.

Functions

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Schemes(X=['4ti2-20061025', 'R-2.6.0', 'atlas-3.7.37', 'atlas-3.8.1', 'a...) source code

Variables

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category_hierarchy = {<class 'sage.categories.category_types.E...

Variables Details

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category_hierarchy

Value:

{<class 'sage.categories.category_types.Elements'>: [<class 'sage.cate
gories.category_types.Sets'>,
                                                     <class 'sage.cate
gories.category_types.Objects'>],
 <class 'sage.categories.category_types.Sequences'>: [<class 'sage.cat
egories.category_types.Sets'>,
                                                      <class 'sage.cat
egories.category_types.Objects'>],
...