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
This data as json, CSV (advanced)
Suggested facets: kind
subcategory | supercategory ▼ | kind |
---|---|---|
CompCat | *Aut | plain |
1 | 1 | contravariant equivalence |
Cat | 2Cat | plain |
DblCat | 2Cat | plain |
Ab | Ab | groups |
AbTor | Ab | plain |
AbTorF | Ab | reflection |
CMon | Ab | plain |
CRing | Ab | commutative monoids |
LieRing | Ab | Lie algebras |
Ring | Ab | monoids |
AdicCRing | AdicRing | plain |
EffAdmRep | AdmRep | plain |
Top | AdmRep | plain |
Top | AdmRep | total restriction |
Set | Ass | plain |
BanAlg | Ban_k | semigroups |
CartSp | Ban_k | plain |
Hilb | Ban_k | full |
Cat | BiCat | plain |
CompBoolAlg | BoolAlg | plain |
SymmMonCat | BrMonCat | full |
SemiLat | CMon | plain |
PROP | CPROP | full |
Field | CRing | full |
DagCat | Cat | plain |
MonCat | Cat | monoids |
Pos | Cat | plain |
Quiv | Cat | full |
RCat | Cat | full |
Set | Cat | plain |
Δ | Cat | full |
DGCAlg | Ch.(Vect_k) | commutative monoids |
CW | Comp | plain |
TopMan | Comp | plain |
FinSet | CompBoolAlg | contravariant equivalence |
DagCompCat | CompCat | plain |
CompBoolAlg | CompLat | plain |
SupLat | CompLat | plain |
BanRing | CompNormGrp | commutative monoids |
CPO | DCPO | plain |
DagCompCat | DagCat | plain |
CartSp | Diff | plain |
BoolAlg | DistLat | plain |
Frm | DistLat | plain |
Ass | Eff | plain |
Δ | FinOrd | plain |
CompBoolAlg | FinSet | contravariant equivalence |
FinGrp | FinSet | groups |
FinOrd | FinSet | skeleton |
Perm | FinSet | core |
FinVect_q | FinVect_k | full |
Mat_k | FinVect_k | equivalence |
Mat_k | FinVect_k | skeleton |
Loc | Frm | contravariant equivalence |
Ab | Grp | groups |
Ab | Grp | reflection |
FinGrp | Grp | full |
Tor | Grp | plain |
Comp | Haus | plain |
Tych | Haus | plain |
BoolAlg | HeytAlg | plain |
FinHilb | Hilb | full |
Hilb | Hilb | contravariant equivalence |
Hilb₀ | Hilb | core |
Ho(Grpd) | Ho(Cat) | full |
EffAdmRep | KV | plain |
SymLMet | LMet | plain |
BoolAlg | Lat | full |
CompLat | Lat | plain |
DistLat | Lat | plain |
Frm | Loc | contravariant equivalence |
SpLoc | Loc | full |
Diff | Man | plain |
LieGrp | Man | groups |
Poiss | Man | plain |
Mat_k | Mat_R | plain |
Mat_R | Mat_SR | plain |
Mat_k | Mat_SR | plain |
FinVect_k | Mat_k | equivalence |
Ban_k | Met | plain |
CompMet | Met | reflection |
Alg(Ab) | Mod(Ab) | monoids |
CommAlg(Ab) | Mod(Ab) | commutative monoids |
Vect_k | Mod(Ab) | full |
Ab | Mon | groups |
CMon | Mon | monoids |
Grp | Mon | plain |
BrMonCat | MonCat | full |
PROP | MonCat | plain |
NormRing | NormGrp | commutative monoids |
Man | PDiff | plain |
PL | PDiff | equivalence |
PDiff | PL | equivalence |
Perm | Perm | contravariant equivalence |
Set | Pfn | total restriction |
Set* | Pfn | equivalence |
DCPO | Pos | plain |
HeytAlg | Pos | plain |
Lat | 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;