name,objects_hr,arrows_hr
□,the inhabited cubes,cubical maps
Ω,the inhabited trees,tree maps
Δ,the inhabited simplices,monotone maps
nCob,(n-1)-dimensional compact oriented manifolds,n-dimensional cobordisms
Vect_k,vector spaces over fields k,linear maps
Tych,Tychonoff spaces,continuous maps
TracedSymmMonCat,traced symmetric monoidal categories,lax monoidal functors
Tor,Torsion groups,group maps
Topos,topoi,geometric arrows
TopVect,topological vector spaces,linear maps
TopRing,topological rings,continuous ring maps
TopMon,topological monoids,continuous monoid maps
TopMan,topological manifolds,continuous maps
TopGrp,topological groups,continuous group maps
TopCat,topologically enriched categories,continuous functors
Top*,pointed topological spaces,based continuous maps
Top,topological spaces,continuous maps
SymmRel,sets,symmetric relations
SymmMonCat,symmetric monoidal categories,lax monoidal functors
SymLMet,symmetric Lawvere metric spaces,short maps
SymCat,symmetric monoidal categories,lax monoidal functors
Surj,sets,surjections
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
SupLat,suplattices,suplattice maps
Stone,Stone spaces,continuous maps
Ste,stereotype spaces,continuous maps
Spectra,topological spectra,spectrum maps
Species,species,natural transformations
Span(Set),sets,spans of functions
Span(Grpd),groupoids,spans of tame functors
SpLoc,spatial locales,continuous maps
SoberTop,sober topological spaces,continuous maps
SimpCat,simplicially enriched categories,simplicially enriched functors
Sierp,maps,commuting squares
Set*,pointed sets,based maps
Set,sets,maps
SemiRing,semirings (rigs),semiring maps
SemiLat,semilattices,semilattice maps
SemiGrp,semigroups,semigroup maps
STopGrp,simplicial topological groups,continuous group maps
STop,simplicial topological spaces,continuous maps
SSet,simplicial sets,simplicial maps
SRing,simplicial rings,ring maps
SMan,simplicial smooth manifolds,smooth maps
SLieAlg_k,simplicial Lie algebras over vector spaces over fields k,linear maps
SGrp,simplicial groups,group maps
SES(Ab),short exact sequences of Abelian groups,commuting diagrams
SAb,simplicial Abelian groups,group maps
Rng,nonunital rings,nonunital ring maps
Ring,rings,ring maps
Rex,finitely cocomplete categories,right exact functors
Rel,sets,relations
RT(K₂),sequences of natural numbers,partial realizable maps
RT(K₁),the natural numbers,partial realizable maps
RCat,restriction categories,functors
R+,non-negative real numbers,addition
Quiv,quivers,graph maps
Quant,quantales,suplattice maps
PseudoMet,pseudometric spaces,short maps
Pros,preorders,monotone maps
Prof,categories,profunctors
PreOrd,preorders,monotone maps
PrCat,locally presentable categories,left adjoint functors
Pos,partial orders,monotone maps
Poiss,smooth manifolds with Poisson structures,Poisson maps
Pfn,sets,partial maps
PermCat,permutative (symmetric strict monoidal) categories,multilinear functors
Perm,the natural numbers,permutations
PROP,monoidal product & permutation categories,eso strict monoidal functors
PL,piecewise-linear manifolds,piecewise-continuous maps
PDiff,piecewise-differentiable manifolds,piecewise-continuous maps
Operad,symmetric multicategories,multifunctors
Op(FinCartSp),open sets of finite-dimensional Cartesian spaces,inclusions
NormRing,normed (commutative) rings,short group maps
NormGrp,normed groups,short group maps
NormAb,normed Abelian groups,group maps
MultiSet,multisets,multimaps
Mono,injections,commuting squares
MonCat,monoidal categories,lax monoidal functors
Mon,monoids,monoid maps
Mod(Ab),modules of monoids in Ab (rings),module maps
Met,metric spaces,short maps
Meas,measurable spaces,measurable maps
Mat_k,the natural numbers,matrices over fields k
Mat_SR,the natural numbers,matrices over semirings SR
Mat_R,the natural numbers,matrices over rings R
Man,smooth manifolds,smooth maps
Log,topoi,logical functors
Loc,locales,continuous maps
LieRing,Lie rings,group maps
LieGrp,Lie groups,smooth group maps
LieAlg_k,Lie algebras over vector spaces over fields k,linear maps
Lex,finitely complete categories,left exact functors
Lat,lattices,lattice maps
LMet,Lawvere metric spaces,short maps
KV,computable real numbers,computable maps
Inj,sets,injections
Idem,idempotent endofunctions,idempotency-respecting maps
I,two objects,the walking isomorphism (and two identity arrows)
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