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