All Subcategories

A subcategory has some of the objects and arrows of its parent category. There are several common special cases:

• Full subcategories have all of the parent category's arrows.
• Essentially wide subcategories have all of the parent category's objects.

2 rows where kind = "total restriction"

✎ View and edit SQL

This data as json, CSV (advanced)

CREATE VIEW "all_subcategories" AS select subcategory, parent as supercategory, 'plain' as kind from subcategories
UNION
select * from all_essentially_wide_subcategories
union
select * from all_full_subcategories
union
select cat1, cat2, 'equivalence' from equivalent_categories
UNION
select cat2, cat1, 'equivalence' from equivalent_categories
UNION
select category, op, 'contravariant equivalence' from opposite_categories
UNION
select op, category, 'contravariant equivalence' from opposite_categories
UNION
select internal_abelian_groups, parent, 'Abelian groups' from categories_of_abelian_groups
union
select internal_commutative_monoids, parent, 'commutative monoids' from categories_of_commutative_monoids
union
select internal_groups, parent, 'groups' from categories_of_groups
union
select internal_lie_algebras, parent, 'Lie algebras' from categories_of_lie_algebras
union
select internal_monoids, parent, 'monoids' from categories_of_monoids
union
select internal_rings, parent, 'rings' from categories_of_rings
union
select internal_semigroups, parent, 'semigroups' from categories_of_semigroups;