name,objects_hr,arrows_hr
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
Inj,sets,injections
Pfn,sets,partial maps
Rel,sets,relations
Set,sets,maps
Span(Set),sets,spans of functions
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
Circ,the natural numbers,Boolean circuits
G,the natural numbers,globe 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
Perm,the natural numbers,permutations
RT(K₁),the natural numbers,partial realizable maps
Log,topoi,logical functors
Topos,topoi,geometric arrows
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)