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.

78 rows where kind = "plain" sorted by supercategory

descending

subcategory	supercategory ▼	kind
CompCat	*Aut	plain
Cat	2Cat	plain
DblCat	2Cat	plain
AbTor	Ab	plain
CMon	Ab	plain
AdicCRing	AdicRing	plain
EffAdmRep	AdmRep	plain
Top	AdmRep	plain
Set	Ass	plain
CartSp	Ban_k	plain
Cat	BiCat	plain
CompBoolAlg	BoolAlg	plain
SemiLat	CMon	plain
DagCat	Cat	plain
Pos	Cat	plain
Set	Cat	plain
CW	Comp	plain
TopMan	Comp	plain
DagCompCat	CompCat	plain
CompBoolAlg	CompLat	plain
SupLat	CompLat	plain
CPO	DCPO	plain
DagCompCat	DagCat	plain
CartSp	Diff	plain
BoolAlg	DistLat	plain
Frm	DistLat	plain
Ass	Eff	plain
Δ	FinOrd	plain
Tor	Grp	plain
Comp	Haus	plain
Tych	Haus	plain
BoolAlg	HeytAlg	plain
EffAdmRep	KV	plain
SymLMet	LMet	plain
CompLat	Lat	plain
DistLat	Lat	plain
Diff	Man	plain
Poiss	Man	plain
Mat_k	Mat_R	plain
Mat_R	Mat_SR	plain
Mat_k	Mat_SR	plain
Ban_k	Met	plain
Grp	Mon	plain
PROP	MonCat	plain
Man	PDiff	plain
DCPO	Pos	plain
HeytAlg	Pos	plain
Lat	Pos	plain
SemiLat	Pos	plain
Δ	Pos	plain
Met	PseudoMet	plain
DGph	Quiv	plain
Eff	RT(K₁)	plain
AdmRep	RT(K₂)	plain
KV	RT(K₂)	plain
Ring	Rng	plain
SMan	STop	plain
Mon	SemiGrp	plain
Lat	SemiLat	plain
Ring	SemiRing	plain
Aut	Set	plain
Pos	Set	plain
Pros	Set	plain
SemiRing	Set	plain
Top	Set	plain
CMon	Set*	plain
Set	Set*	plain
Frm	SupLat	plain
PseudoMet	SymLMet	plain
*Aut	SymmMonCat	plain
TracedSymmMonCat	SymmMonCat	plain
LMet	Top	plain
PDiff	Top	plain
TopVect	Top	plain
AdicRing	TopRing	plain
AbTor	Tor	plain
CompCat	TracedSymmMonCat	plain
CartSp	Vect_k	plain

Advanced export

JSON shape: default, array, newline-delimited

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;

All Subcategories

all_subcategories (view)

78 rows where kind = "plain" sorted by supercategory

Advanced export