All Subcategories

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

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Suggested facets: kind

subcategory supercategory kind
*Aut SymmMonCat plain
1 1 contravariant equivalence
Ab Ab groups
Ab Grp groups
Ab Grp reflection
Ab Mon groups
Ab Set Abelian groups
AbTor Ab plain
AbTor Tor plain
AbTorF Ab reflection
AdicCRing AdicRing plain
AdicRing TopRing plain
AdmRep RT(K₂) plain
Alg(Ab) Mod(Ab) monoids
Ass Eff plain
Aut Set plain
BanAlg Ban_k semigroups
BanRing CompNormGrp commutative monoids
Ban_k Met plain
Ban_k Ste full
Bij Set core
BoolAlg DistLat plain
BoolAlg HeytAlg plain
BoolAlg Lat full
BrMonCat MonCat full
CMon Ab plain
CMon Mon monoids
CMon Set commutative monoids
CMon Set* plain
CPO DCPO plain
CRing Ab commutative monoids
CRing Ring reflection
CW Comp plain
CartSp Ban_k plain
CartSp Diff plain
CartSp Vect_k plain
Cat 2Cat plain
Cat BiCat plain
Cat SSet reflection
CommAlg(Ab) Mod(Ab) commutative monoids
Comp Haus plain
Comp Top reflection
CompBoolAlg BoolAlg plain
CompBoolAlg CompLat plain
CompBoolAlg FinSet contravariant equivalence
CompCat *Aut plain
CompCat TracedSymmMonCat plain
CompLat Lat plain
CompMet Met reflection
DCPO Pos plain
DGCAlg Ch.(Vect_k) commutative monoids
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
Field CRing full
FinGrp FinSet groups
FinGrp Grp full
FinHilb Hilb full
FinOrd FinSet skeleton
FinSet CompBoolAlg contravariant equivalence
FinSet Set full
FinVect_k Mat_k equivalence
FinVect_k Vect_k full
FinVect_q FinVect_k full
Frm DistLat plain
Frm Loc contravariant equivalence
Frm SupLat plain
Grp Mon plain
Grp Set groups
Haus Top full
HeytAlg Pos plain
Hilb Ban_k full
Hilb Hilb contravariant equivalence
Hilb₀ Hilb core
Ho(Grpd) Ho(Cat) full
Inj Set essentially wide
KV RT(K₂) plain
LMet Top plain
Lat Pos plain
Lat SemiLat plain
LieAlg_k Vect_k Lie algebras
LieGrp Man groups
LieRing Ab Lie algebras
Loc Frm contravariant equivalence
Man PDiff plain
Mat_R Mat_SR plain
Mat_k FinVect_k equivalence
Mat_k FinVect_k skeleton
Mat_k Mat_R plain
Mat_k Mat_SR plain
Met PseudoMet plain
Mon SemiGrp plain
Mon Set monoids

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CREATE VIEW "all_subcategories" AS select subcategory, parent as supercategory, 'plain' as kind from subcategories
select * from all_essentially_wide_subcategories
select * from all_full_subcategories
select cat1, cat2, 'equivalence' from equivalent_categories
select cat2, cat1, 'equivalence' from equivalent_categories
select category, op, 'contravariant equivalence' from opposite_categories
select op, category, 'contravariant equivalence' from opposite_categories
select internal_abelian_groups, parent, 'Abelian groups' from categories_of_abelian_groups
select internal_commutative_monoids, parent, 'commutative monoids' from categories_of_commutative_monoids
select internal_groups, parent, 'groups' from categories_of_groups
select internal_lie_algebras, parent, 'Lie algebras' from categories_of_lie_algebras
select internal_monoids, parent, 'monoids' from categories_of_monoids
select internal_rings, parent, 'rings' from categories_of_rings
select internal_semigroups, parent, 'semigroups' from categories_of_semigroups;