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 kind
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Suggested facets: kind
subcategory | supercategory | kind ▼ |
---|---|---|
Ab | Set | Abelian groups |
SAb | SSet | Abelian groups |
LieAlg_k | Vect_k | Lie algebras |
LieRing | Ab | Lie algebras |
SLieAlg_k | SSet | Lie algebras |
SupLieAlg_k | SupVect_k | Lie algebras |
BanRing | CompNormGrp | commutative monoids |
CMon | Set | commutative monoids |
CRing | Ab | commutative monoids |
CommAlg(Ab) | Mod(Ab) | commutative monoids |
DGCAlg | Ch.(Vect_k) | commutative monoids |
NormRing | NormGrp | commutative monoids |
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 |
Bij | Set | core |
Hilb₀ | Hilb | core |
Perm | FinSet | core |
SymmRel | Rel | core |
FinVect_k | Mat_k | equivalence |
Mat_k | FinVect_k | equivalence |
PDiff | PL | equivalence |
PL | PDiff | equivalence |
Pfn | Set* | equivalence |
Set* | Pfn | equivalence |
SoberTop | SpLoc | equivalence |
SpLoc | SoberTop | equivalence |
Inj | Set | essentially wide |
Pfn | Rel | essentially wide |
Surj | Set | essentially wide |
Ban_k | Ste | full |
BoolAlg | Lat | full |
BrMonCat | MonCat | full |
Field | CRing | full |
FinGrp | Grp | full |
FinHilb | Hilb | full |
FinSet | Set | full |
FinVect_k | Vect_k | full |
FinVect_q | FinVect_k | full |
Haus | Top | full |
Hilb | Ban_k | full |
Ho(Grpd) | Ho(Cat) | full |
PROP | CPROP | full |
Quiv | Cat | full |
RCat | Cat | full |
SoberTop | Top | full |
SpLoc | Loc | full |
Ste | TopVect | full |
SymmMonCat | BrMonCat | full |
Vect_k | Mod(Ab) | full |
Δ | Cat | full |
Ab | Ab | groups |
Ab | Grp | groups |
Ab | Mon | groups |
FinGrp | FinSet | groups |
Grp | Set | groups |
LieGrp | Man | groups |
SGrp | SSet | groups |
TopGrp | Top | groups |
Alg(Ab) | Mod(Ab) | monoids |
CMon | Mon | monoids |
Mon | Set | monoids |
MonCat | Cat | monoids |
Ring | Ab | monoids |
TopMon | Top | monoids |
*Aut | SymmMonCat | plain |
AbTor | Ab | plain |
AbTor | Tor | plain |
AdicCRing | AdicRing | plain |
AdicRing | TopRing | plain |
AdmRep | RT(K₂) | plain |
Ass | Eff | plain |
Aut | Set | plain |
Ban_k | Met | plain |
BoolAlg | DistLat | plain |
BoolAlg | HeytAlg | plain |
CMon | Ab | plain |
CMon | Set* | plain |
CPO | DCPO | plain |
CW | Comp | plain |
CartSp | Ban_k | plain |
CartSp | Diff | plain |
CartSp | Vect_k | plain |
Cat | 2Cat | plain |
Cat | BiCat | plain |
Comp | Haus | plain |
CompBoolAlg | BoolAlg | plain |
CompBoolAlg | CompLat | plain |
CompCat | *Aut | plain |
CompCat | TracedSymmMonCat | plain |
CompLat | Lat | plain |
DCPO | Pos | 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;