All Subcategories

A subcategory has some of the objects and arrows of its parent category. There are several common special cases:

all_subcategories (view)

168 rows sorted by kind

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subcategory supercategory kind ▼
DGph Quiv plain
DagCat Cat plain
DagCompCat CompCat plain
DagCompCat DagCat plain
DblCat 2Cat plain
Diff Man plain
DistLat Lat plain
Eff RT(K₁) plain
EffAdmRep AdmRep plain
EffAdmRep KV plain
Frm DistLat plain
Frm SupLat plain
Grp Mon plain
HeytAlg Pos plain
KV RT(K₂) plain
LMet Top plain
Lat Pos plain
Lat SemiLat plain
Man PDiff plain
Mat_R Mat_SR plain
Mat_k Mat_R plain
Mat_k Mat_SR plain
Met PseudoMet plain
Mon SemiGrp plain
PDiff Top plain
PROP MonCat plain
Poiss Man plain
Pos Cat plain
Pos Set plain
Pros Set plain
PseudoMet SymLMet plain
Ring Rng plain
Ring SemiRing plain
SMan STop plain
SemiLat CMon plain
SemiLat Pos plain
SemiRing Set plain
Set Ass plain
Set Cat plain
Set Set* plain
SupLat CompLat plain
SymLMet LMet plain
Top AdmRep plain
Top Set plain
TopMan Comp plain
TopVect Top plain
Tor Grp plain
TracedSymmMonCat SymmMonCat plain
Tych Haus plain
Δ FinOrd plain
Δ Pos plain
Ab Grp reflection
AbTorF Ab reflection
CRing Ring reflection
Cat SSet reflection
Comp Top reflection
CompMet Met reflection
Ring Set rings
SRing SSet rings
TopRing Top rings
BanAlg Ban_k semigroups
Quant SupLat semigroups
SemiGrp Set semigroups
FinOrd FinSet skeleton
Mat_k FinVect_k skeleton
Pos Pros skeleton
Set Pfn total restriction
Top AdmRep total restriction

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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;