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)
168 rows
This data as json, CSV (advanced)
| subcategory | supercategory | kind |
|---|---|---|
| MonCat | Cat | monoids |
| NormRing | NormGrp | commutative monoids |
| PDiff | PL | equivalence |
| PDiff | Top | plain |
| PL | PDiff | equivalence |
| PROP | CPROP | full |
| PROP | MonCat | plain |
| Perm | FinSet | core |
| Perm | Perm | contravariant equivalence |
| Pfn | Rel | essentially wide |
| Pfn | Set* | equivalence |
| Poiss | Man | plain |
| Pos | Cat | plain |
| Pos | Pros | skeleton |
| Pos | Set | plain |
| Prof | Prof | contravariant equivalence |
| Pros | Set | plain |
| PseudoMet | SymLMet | plain |
| Quant | SupLat | semigroups |
| Quiv | Cat | full |
| RCat | Cat | full |
| Rel | Rel | contravariant equivalence |
| Ring | Ab | monoids |
| Ring | Rng | plain |
| Ring | SemiRing | plain |
| Ring | Set | rings |
| SAb | SSet | Abelian groups |
| SGrp | SSet | groups |
| SLieAlg_k | SSet | Lie algebras |
| SMan | STop | plain |
| SRing | SSet | rings |
| SemiGrp | Set | semigroups |
| SemiLat | CMon | plain |
| SemiLat | Pos | plain |
| SemiRing | Set | plain |
| Set | Ass | plain |
| Set | Cat | plain |
| Set | Pfn | total restriction |
| Set | Set* | plain |
| Set* | Pfn | equivalence |
| SoberTop | SpLoc | equivalence |
| SoberTop | Top | full |
| SpLoc | Loc | full |
| SpLoc | SoberTop | equivalence |
| Span(Set) | Span(Set) | contravariant equivalence |
| Ste | TopVect | full |
| SupLat | CompLat | plain |
| SupLieAlg_k | SupVect_k | Lie algebras |
| Surj | Set | essentially wide |
| SymLMet | LMet | plain |
| SymmMonCat | BrMonCat | full |
| SymmRel | Rel | core |
| Top | AdmRep | plain |
| Top | AdmRep | total restriction |
| Top | Set | plain |
| TopGrp | Top | groups |
| TopMan | Comp | plain |
| TopMon | Top | monoids |
| TopRing | Top | rings |
| TopVect | Top | plain |
| Tor | Grp | plain |
| TracedSymmMonCat | SymmMonCat | plain |
| Tych | Haus | plain |
| Vect_k | Mod(Ab) | full |
| nCob | nCob | contravariant equivalence |
| Δ | Cat | full |
| Δ | FinOrd | plain |
| Δ | Pos | plain |
Advanced export
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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;