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 subcategory descending
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Suggested facets: kind
subcategory ▲ | supercategory | kind |
---|---|---|
Δ | Cat | full |
Δ | FinOrd | plain |
Δ | Pos | plain |
nCob | nCob | contravariant equivalence |
Vect_k | Mod(Ab) | full |
Tych | Haus | plain |
TracedSymmMonCat | SymmMonCat | plain |
Tor | Grp | plain |
TopVect | Top | plain |
TopRing | Top | rings |
TopMon | Top | monoids |
TopMan | Comp | plain |
TopGrp | Top | groups |
Top | AdmRep | plain |
Top | AdmRep | total restriction |
Top | Set | plain |
SymmRel | Rel | core |
SymmMonCat | BrMonCat | full |
SymLMet | LMet | plain |
Surj | Set | essentially wide |
SupLieAlg_k | SupVect_k | Lie algebras |
SupLat | CompLat | plain |
Ste | TopVect | full |
Span(Set) | Span(Set) | contravariant equivalence |
SpLoc | Loc | full |
SpLoc | SoberTop | equivalence |
SoberTop | SpLoc | equivalence |
SoberTop | Top | full |
Set* | Pfn | equivalence |
Set | Ass | plain |
Set | Cat | plain |
Set | Pfn | total restriction |
Set | Set* | plain |
SemiRing | Set | plain |
SemiLat | CMon | plain |
SemiLat | Pos | plain |
SemiGrp | Set | semigroups |
SRing | SSet | rings |
SMan | STop | plain |
SLieAlg_k | SSet | Lie algebras |
SGrp | SSet | groups |
SAb | SSet | Abelian groups |
Ring | Ab | monoids |
Ring | Rng | plain |
Ring | SemiRing | plain |
Ring | Set | rings |
Rel | Rel | contravariant equivalence |
RCat | Cat | full |
Quiv | Cat | full |
Quant | SupLat | semigroups |
PseudoMet | SymLMet | plain |
Pros | Set | plain |
Prof | Prof | contravariant equivalence |
Pos | Cat | plain |
Pos | Pros | skeleton |
Pos | Set | plain |
Poiss | Man | plain |
Pfn | Rel | essentially wide |
Pfn | Set* | equivalence |
Perm | FinSet | core |
Perm | Perm | contravariant equivalence |
PROP | CPROP | full |
PROP | MonCat | plain |
PL | PDiff | equivalence |
PDiff | PL | equivalence |
PDiff | Top | plain |
NormRing | NormGrp | commutative monoids |
MonCat | Cat | monoids |
Mon | SemiGrp | plain |
Mon | Set | monoids |
Met | PseudoMet | plain |
Mat_k | FinVect_k | equivalence |
Mat_k | FinVect_k | skeleton |
Mat_k | Mat_R | plain |
Mat_k | Mat_SR | plain |
Mat_R | Mat_SR | plain |
Man | PDiff | plain |
Loc | Frm | contravariant equivalence |
LieRing | Ab | Lie algebras |
LieGrp | Man | groups |
LieAlg_k | Vect_k | Lie algebras |
Lat | Pos | plain |
Lat | SemiLat | plain |
LMet | Top | plain |
KV | RT(K₂) | plain |
Inj | Set | essentially wide |
Ho(Grpd) | Ho(Cat) | full |
Hilb₀ | Hilb | core |
Hilb | Ban_k | full |
Hilb | Hilb | contravariant equivalence |
HeytAlg | Pos | plain |
Haus | Top | full |
Grp | Mon | plain |
Grp | Set | groups |
Frm | DistLat | plain |
Frm | Loc | contravariant equivalence |
Frm | SupLat | plain |
FinVect_q | FinVect_k | full |
FinVect_k | Mat_k | equivalence |
FinVect_k | Vect_k | full |
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;