#10963: More functorial constructions
-------------------------------------+-------------------------------------
Reporter: nthiery | Owner: stumpc5
Type: enhancement | Status: needs_work
Priority: major | Milestone:
Component: categories | Resolution:
Keywords: | Merged in:
Authors: Nicolas M. Thiéry | Reviewers: Simon King
Report Upstream: N/A | Work issues: Reduce startup time
Branch: | by 5%. Avoid "recursion depth
Dependencies: #11224, #8327, | exceeded (ignored)".
#10193, #12895, #14516, #14722, | Commit:
#13589 | Stopgaps:
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Description changed by nthiery:
Old description:
> This ticket implements:
>
> - Support for full subcategories defined by an axiom (Finite,
> Infinite, FiniteDimensional, Commutative, Associative, Unital,
> Inverse, NoZeroDivisors, Division, Facade), and joins thereof:
>
> {{{
> sage: Groups() & Sets().Finite()
> Category of finite groups
> sage: Algebras(QQ).Finite() & Monoids().Commutative()
> Join of Category of commutative algebras over Rational Field and
> Category of finite monoids
> sage: Rings().Division() & Sets().Finite()
> Category of finite fields
> }}}
>
> - New categories:
> - AdditiveSemigroups, AdditiveMonoids, AdditiveGroups
> - DistributiveMagmasAndAdditiveMagmas
> - MagmaticAlgebras (will replace Algebras in #15043)
> - AssociativeAlgebras
> - UnitalAlgebras
> - Algebras of additive semigroups and monoids
>
> - More mathematical rules:
> - A subquotient of a finite set is a finite set
> - The algebra of a finite set is finite dimensional
> - The algebra of a commutative magma is commutative
> - A finite division ring is a field
> - ...
>
> - More documentation for IsomorphicObjects and other doc improvements
>
> - Complete revamping of sage.categories.primer
>
> - Use SubcategoryMethods to put the functorial constructions where
> they belong. E.g. DualObjects, TensorProducts, and Graded are now
> only defined for subcategories of Modules.
>
> Patch developed on:
> http://combinat.sagemath.org/patches/file/tip/trac_10963
> -more_functorial_constructions-nt.patch.
New description:
This ticket implements:
- Support for full subcategories defined by an axiom (Finite,
Infinite, Facade, Commutative, Associative, Unital,
Inverse, NoZeroDivisors, Division, FiniteDimensional, Connected,
WithBasis, Irreducible), and joins thereof:
{{{
sage: Groups() & Sets().Finite()
Category of finite groups
sage: Algebras(QQ).Finite() & Monoids().Commutative()
Join of Category of commutative algebras over Rational Field and
Category of finite monoids
sage: Rings().Division() & Sets().Finite()
Category of finite fields
}}}
- New categories:
- AdditiveSemigroups, AdditiveMonoids, AdditiveGroups
- DistributiveMagmasAndAdditiveMagmas
- MagmaticAlgebras (will replace Algebras in #15043)
- AssociativeAlgebras
- UnitalAlgebras
- Algebras of additive semigroups and monoids
- More mathematical rules:
- A subquotient of a finite set is a finite set
- The algebra of a finite set is finite dimensional
- The algebra of a commutative magma is commutative
- A finite division ring is a field
- ...
- More documentation for IsomorphicObjects and other doc improvements
- Complete revamping of sage.categories.primer
- Use SubcategoryMethods to put the functorial constructions where
they belong. E.g. DualObjects, TensorProducts, and Graded are now
only defined for subcategories of Modules.
Patch developed on:
http://combinat.sagemath.org/patches/file/tip/trac_10963
-more_functorial_constructions-nt.patch.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:80>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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