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.
all_subcategories (view)
11 rows where kind = "contravariant equivalence"
This data as json, CSV (advanced)
| subcategory | supercategory | kind |
|---|---|---|
| 1 | 1 | contravariant equivalence |
| CompBoolAlg | FinSet | contravariant equivalence |
| FinSet | CompBoolAlg | contravariant equivalence |
| Frm | Loc | contravariant equivalence |
| Hilb | Hilb | contravariant equivalence |
| Loc | Frm | contravariant equivalence |
| Perm | Perm | contravariant equivalence |
| Prof | Prof | contravariant equivalence |
| Rel | Rel | contravariant equivalence |
| Span(Set) | Span(Set) | contravariant equivalence |
| nCob | nCob | contravariant equivalence |
Advanced export
JSON shape: default, array, newline-delimited
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;