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