name,objects_hr,arrows_hr
1,(is) the point,(is) the identity arrow
2Cat,2-categories,2-functors
Circ,the natural numbers,Boolean circuits
Poiss,smooth manifolds with Poisson structures,Poisson maps
DCPO,directed-complete partial orders,Scott-continuous maps
CPO,complete partial orders,Scott-continuous maps
R+,non-negative real numbers,addition
Alg(Ab),algebras of monoids in Ab (rings),algebra maps
CommAlg(Ab),commutative algebras of monoids in Ab (rings),algebra maps
Top*,pointed topological spaces,based continuous maps
Set*,pointed sets,based maps
Bij,sets,bijections
Bimod(Ab),monoids in Ab (rings),bimodules of monoids in Ab (rings)
CW,CW complexes,cellular maps
SES(Ab),short exact sequences of Abelian groups,commuting diagrams
Mono,injections,commuting squares
Sierp,maps,commuting squares
EffAdmRep,effective admissible domain representations,computable continuous maps
Eff,sets with computable equality,computable maps
Ass,assemblies,computable maps
KV,computable real numbers,computable maps
TopCat,topologically enriched categories,continuous functors
TopGrp,topological groups,continuous group maps
STopGrp,simplicial topological groups,continuous group maps
Comp,compacta (compact Hausdorff spaces),continuous maps
Diff,differentiable manifolds,continuous maps
Loc,locales,continuous maps
Top,topological spaces,continuous maps
TopMan,topological manifolds,continuous maps
Haus,Hausdorff (T₂) spaces,continuous maps
Tych,Tychonoff spaces,continuous maps
Stone,Stone spaces,continuous maps
STop,simplicial topological spaces,continuous maps
SoberTop,sober topological spaces,continuous maps
SpLoc,spatial locales,continuous maps
Ste,stereotype spaces,continuous maps
1Type,homotopy 1-types,continuous maps
TopMon,topological monoids,continuous monoid maps
TopRing,topological rings,continuous ring maps
AdicRing,adic rings,continuous ring maps
AdicCRing,commutative adic rings,continuous ring maps
□,the inhabited cubes,cubical maps
DSet,dendroidal sets,dendroidal maps
DGCAlg,differential-graded commutative algebras of vector spaces,differential-graded algebra maps
DGph,digraphs,digraph maps
DblCat,double categories,double functors
PROP,monoidal product & permutation categories,eso strict monoidal functors
CPROP,colored monoidal product & permutation categories,eso strict monoidal functors
Field,fields,field maps
FinSet,finite sets,finite maps
Frm,frames,frame maps
Cat,categories,functors
Grpd,groupoids,functors
RCat,restriction categories,functors
Topos,topoi,geometric arrows
G,the natural numbers,globe maps
DirGph,directed graphs,graph maps
Gph,undirected graphs,graph maps
Quiv,quivers,graph maps
Ab,Abelian groups,group maps
FinGrp,finite groups,group maps
Grp,groups,group maps
NormAb,normed Abelian groups,group maps
Tor,Torsion groups,group maps
AbTor,Abelian torsion groups,group maps
AbTorF,torsion-free Abelian groups,group maps
SGrp,simplicial groups,group maps
SAb,simplicial Abelian groups,group maps
LieRing,Lie rings,group maps
Ho(Eff),numbered sets,homotopy classes of computable maps
Ho(Top),topological spaces,homotopy classes of continuous maps
Hyp,finite directed hypergraphs,hypergraph maps
Idem,idempotent endofunctions,idempotency-respecting maps
Op(FinCartSp),open sets of finite-dimensional Cartesian spaces,inclusions
Inj,sets,injections
BoolAlg,Boolean algebras,lattice maps
CompBoolAlg,complete Boolean algebras (CABAs),lattice maps
CompLat,complete lattices,lattice maps
DistLat,distributive lattices,lattice maps
HeytAlg,Heyting algebras,lattice maps
Lat,lattices,lattice maps
MonCat,monoidal categories,lax monoidal functors
SymCat,symmetric monoidal categories,lax monoidal functors
BrMonCat,braided monoidal categories,lax monoidal functors
SymmMonCat,symmetric monoidal categories,lax monoidal functors
TracedSymmMonCat,traced symmetric monoidal categories,lax monoidal functors
CompCat,compact closed categories,lax monoidal functors
*Aut,star-autonomous categories,lax monoidal functors
DagCompCat,compact closed †-categories,lax monoidal †-functors
PrCat,locally presentable categories,left adjoint functors
Lex,finitely complete categories,left exact functors
Ch.(Vect_k),chain complices of vector spaces,linear maps
FinVect_k,finite vector spaces over fields k,linear maps
Vect_k,vector spaces over fields k,linear maps
TopVect,topological vector spaces,linear maps
LieAlg_k,Lie algebras over vector spaces over fields k,linear maps
SLieAlg_k,simplicial Lie algebras over vector spaces over fields k,linear maps
FinVect_q,finite vector spaces over finite fields of order q,linear maps
Log,topoi,logical functors
Set,sets,maps
Mat_k,the natural numbers,matrices over fields k
Mat_R,the natural numbers,matrices over rings R
Mat_SR,the natural numbers,matrices over semirings SR
Meas,measurable spaces,measurable maps
Mod(Ab),modules of monoids in Ab (rings),module maps
CMon,commutative monoids,monoid maps
Mon,monoids,monoid maps
Pos,partial orders,monotone maps
PreOrd,preorders,monotone maps
Δ,the inhabited simplices,monotone maps
Pros,preorders,monotone maps
Operad,symmetric multicategories,multifunctors
PermCat,permutative (symmetric strict monoidal) categories,multilinear functors
MultiSet,multisets,multimaps
nCob,(n-1)-dimensional compact oriented manifolds,n-dimensional cobordisms
Ho(Cat),categories,natural isomorphism classes of functors
Ho(Grpd),groupoids,natural isomorphism classes of functors
Species,species,natural transformations
Cluster,partitioned sets,non-refinement-increasing maps
Rng,nonunital rings,nonunital ring maps
FinOrd,the finite ordinal numbers,order-preserving maps
Pfn,sets,partial maps
RT(K₁),the natural numbers,partial realizable maps
RT(K₂),sequences of natural numbers,partial realizable maps
Perm,the natural numbers,permutations
PL,piecewise-linear manifolds,piecewise-continuous maps
PDiff,piecewise-differentiable manifolds,piecewise-continuous maps
Prof,categories,profunctors
BiCat,bicategories,pseudofunctors
Rel,sets,relations
AdmRep,admissible domain representations,representable continuous maps
Rex,finitely cocomplete categories,right exact functors
AbCat,Abelian categories,right exact functors
CRing,commutative rings,ring maps
Ring,rings,ring maps
SRing,simplicial rings,ring maps
SemiGrp,semigroups,semigroup maps
SemiLat,semilattices,semilattice maps
SemiRing,semirings (rigs),semiring maps
NormGrp,normed groups,short group maps
NormRing,normed (commutative) rings,short group maps
BanRing,Banach rings,short group maps
CompNormGrp,complete normed groups,short group maps
Ban_k,Banach spaces over fields k,short linear maps
FinHilb,finite-dimensional Hilbert spaces,short linear maps
Hilb,Hilbert spaces,short linear maps
BanAlg,Banach algebras,short linear maps
Met,metric spaces,short maps
FinMet,finite metric spaces,short maps
PseudoMet,pseudometric spaces,short maps
LMet,Lawvere metric spaces,short maps
SymLMet,symmetric Lawvere metric spaces,short maps
CompMet,complete metric spaces,short maps
SSet,simplicial sets,simplicial maps
SimpCat,simplicially enriched categories,simplicially enriched functors
Aut,regular (Moore) automata,simulations
LieGrp,Lie groups,smooth group maps
CartSp,Cartesian spaces,smooth maps
Man,smooth manifolds,smooth maps
SMan,simplicial smooth manifolds,smooth maps
Span(Set),sets,spans of functions
Span(Grpd),groupoids,spans of tame functors
Spectra,topological spectra,spectrum maps
SupVect_k,super vector spaces over fields k,super linear maps
SupLieAlg_k,Lie algebras over super vector spaces over fields k,super linear maps
Quant,quantales,suplattice maps
SupLat,suplattices,suplattice maps
Surj,sets,surjections
SymmRel,sets,symmetric relations
Feyn,Feynman diagrams,symmetries of Feynman diagrams
2,two objects,the walking arrow (and two identity arrows)
I,two objects,the walking isomorphism (and two identity arrows)
Ω,the inhabited trees,tree maps
Hilb₀,Hilbert spaces,unitary operators
DagCat,†-categories (dagger categories),†-functors (dagger functors)