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 sorted by supercategory descending
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Suggested facets: kind
| subcategory | supercategory ▲ | kind |
|---|---|---|
| nCob | nCob | contravariant equivalence |
| CartSp | Vect_k | plain |
| FinVect_k | Vect_k | full |
| LieAlg_k | Vect_k | Lie algebras |
| CompCat | TracedSymmMonCat | plain |
| AbTor | Tor | plain |
| Ste | TopVect | full |
| AdicRing | TopRing | plain |
| Comp | Top | reflection |
| Haus | Top | full |
| LMet | Top | plain |
| PDiff | Top | plain |
| SoberTop | Top | full |
| TopGrp | Top | groups |
| TopMon | Top | monoids |
| TopRing | Top | rings |
| TopVect | Top | plain |
| *Aut | SymmMonCat | plain |
| TracedSymmMonCat | SymmMonCat | plain |
| PseudoMet | SymLMet | plain |
| SupLieAlg_k | SupVect_k | Lie algebras |
| Frm | SupLat | plain |
| Quant | SupLat | semigroups |
| Ban_k | Ste | full |
| Span(Set) | Span(Set) | contravariant equivalence |
| SoberTop | SpLoc | equivalence |
| SpLoc | SoberTop | equivalence |
| CMon | Set* | plain |
| Pfn | Set* | equivalence |
| Set | Set* | plain |
| Ab | Set | Abelian groups |
| Aut | Set | plain |
| Bij | Set | core |
| CMon | Set | commutative monoids |
| FinSet | Set | full |
| Grp | Set | groups |
| Inj | Set | essentially wide |
| Mon | Set | monoids |
| Pos | Set | plain |
| Pros | Set | plain |
| Ring | Set | rings |
| SemiGrp | Set | semigroups |
| SemiRing | Set | plain |
| Surj | Set | essentially wide |
| Top | Set | plain |
| Ring | SemiRing | plain |
| Lat | SemiLat | plain |
| Mon | SemiGrp | plain |
| SMan | STop | plain |
| Cat | SSet | reflection |
| SAb | SSet | Abelian groups |
| SGrp | SSet | groups |
| SLieAlg_k | SSet | Lie algebras |
| SRing | SSet | rings |
| Ring | Rng | plain |
| CRing | Ring | reflection |
| Pfn | Rel | essentially wide |
| Rel | Rel | contravariant equivalence |
| SymmRel | Rel | core |
| AdmRep | RT(K₂) | plain |
| KV | RT(K₂) | plain |
| Eff | RT(K₁) | plain |
| DGph | Quiv | plain |
| Met | PseudoMet | plain |
| Pos | Pros | skeleton |
| Prof | Prof | contravariant equivalence |
| DCPO | Pos | plain |
| HeytAlg | Pos | plain |
| Lat | Pos | plain |
| SemiLat | Pos | plain |
| Δ | Pos | plain |
| Set | Pfn | total restriction |
| Set* | Pfn | equivalence |
| Perm | Perm | contravariant equivalence |
| PDiff | PL | equivalence |
| Man | PDiff | plain |
| PL | PDiff | equivalence |
| NormRing | NormGrp | commutative monoids |
| BrMonCat | MonCat | full |
| PROP | MonCat | plain |
| Ab | Mon | groups |
| CMon | Mon | monoids |
| Grp | Mon | plain |
| Alg(Ab) | Mod(Ab) | monoids |
| CommAlg(Ab) | Mod(Ab) | commutative monoids |
| Vect_k | Mod(Ab) | full |
| Ban_k | Met | plain |
| CompMet | Met | reflection |
| FinVect_k | Mat_k | equivalence |
| Mat_R | Mat_SR | plain |
| Mat_k | Mat_SR | plain |
| Mat_k | Mat_R | plain |
| Diff | Man | plain |
| LieGrp | Man | groups |
| Poiss | Man | plain |
| Frm | Loc | contravariant equivalence |
| SpLoc | Loc | full |
| BoolAlg | Lat | full |
| CompLat | Lat | plain |
| DistLat | Lat | plain |
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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;