name,objects_hr,arrows_hr
Hyp,finite directed hypergraphs,hypergraph maps
Ho(Top),topological spaces,homotopy classes of continuous maps
Ho(Grpd),groupoids,natural isomorphism classes of functors
Ho(Eff),numbered sets,homotopy classes of computable maps
Ho(Cat),categories,natural isomorphism classes of functors
Hilb₀,Hilbert spaces,unitary operators
Hilb,Hilbert spaces,short linear maps
HeytAlg,Heyting algebras,lattice maps
Haus,Hausdorff (T₂) spaces,continuous maps
Grpd,groupoids,functors
Grp,groups,group maps
Gph,undirected graphs,graph maps
G,the natural numbers,globe maps
Frm,frames,frame maps
FinVect_q,finite vector spaces over finite fields of order q,linear maps
FinVect_k,finite vector spaces over fields k,linear maps
FinSet,finite sets,finite maps
FinOrd,the finite ordinal numbers,order-preserving maps
FinMet,finite metric spaces,short maps
FinHilb,finite-dimensional Hilbert spaces,short linear maps
FinGrp,finite groups,group maps
Field,fields,field maps
Feyn,Feynman diagrams,symmetries of Feynman diagrams
EffAdmRep,effective admissible domain representations,computable continuous maps
Eff,sets with computable equality,computable maps
DistLat,distributive lattices,lattice maps
DirGph,directed graphs,graph maps
Diff,differentiable manifolds,continuous maps
DblCat,double categories,double functors
DagCompCat,compact closed †-categories,lax monoidal †-functors
DagCat,†-categories (dagger categories),†-functors (dagger functors)
DSet,dendroidal sets,dendroidal maps
DGph,digraphs,digraph maps
DGCAlg,differential-graded commutative algebras of vector spaces,differential-graded algebra maps
DCPO,directed-complete partial orders,Scott-continuous maps
CompNormGrp,complete normed groups,short group maps
CompMet,complete metric spaces,short maps
CompLat,complete lattices,lattice maps
CompCat,compact closed categories,lax monoidal functors
CompBoolAlg,complete Boolean algebras (CABAs),lattice maps
Comp,compacta (compact Hausdorff spaces),continuous maps
CommAlg(Ab),commutative algebras of monoids in Ab (rings),algebra maps
Cluster,partitioned sets,non-refinement-increasing maps
Circ,the natural numbers,Boolean circuits
Ch.(Vect_k),chain complices of vector spaces,linear maps
Cat,categories,functors
CartSp,Cartesian spaces,smooth maps
CW,CW complexes,cellular maps
CRing,commutative rings,ring maps
CPROP,colored monoidal product & permutation categories,eso strict monoidal functors
CPO,complete partial orders,Scott-continuous maps
CMon,commutative monoids,monoid maps
BrMonCat,braided monoidal categories,lax monoidal functors
BoolAlg,Boolean algebras,lattice maps
Bimod(Ab),monoids in Ab (rings),bimodules of monoids in Ab (rings)
Bij,sets,bijections
BiCat,bicategories,pseudofunctors
Ban_k,Banach spaces over fields k,short linear maps
BanRing,Banach rings,short group maps
BanAlg,Banach algebras,short linear maps
Aut,regular (Moore) automata,simulations
Ass,assemblies,computable maps
Alg(Ab),algebras of monoids in Ab (rings),algebra maps
AdmRep,admissible domain representations,representable continuous maps
AdicRing,adic rings,continuous ring maps
AdicCRing,commutative adic rings,continuous ring maps
AbTorF,torsion-free Abelian groups,group maps
AbTor,Abelian torsion groups,group maps
AbCat,Abelian categories,right exact functors
Ab,Abelian groups,group maps
2Cat,2-categories,2-functors
2,two objects,the walking arrow (and two identity arrows)
1Type,homotopy 1-types,continuous maps
1,(is) the point,(is) the identity arrow
*Aut,star-autonomous categories,lax monoidal functors