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