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