name,objects_hr,arrows_hr
Mat_k,the natural numbers,matrices over fields k
Mat_R,the natural numbers,matrices over rings R
Mat_SR,the natural numbers,matrices over semirings SR
Meas,measurable spaces,measurable maps
Mod(Ab),modules of monoids in Ab (rings),module maps
CMon,commutative monoids,monoid maps
Mon,monoids,monoid maps
Pos,partial orders,monotone maps
PreOrd,preorders,monotone maps
Pros,preorders,monotone maps
Δ,the inhabited simplices,monotone maps
Operad,symmetric multicategories,multifunctors
PermCat,permutative (symmetric strict monoidal) categories,multilinear functors
MultiSet,multisets,multimaps
nCob,(n-1)-dimensional compact oriented manifolds,n-dimensional cobordisms
Ho(Cat),categories,natural isomorphism classes of functors
Ho(Grpd),groupoids,natural isomorphism classes of functors
Species,species,natural transformations
Cluster,partitioned sets,non-refinement-increasing maps
Rng,nonunital rings,nonunital ring maps
FinOrd,the finite ordinal numbers,order-preserving maps
Pfn,sets,partial maps
RT(K₁),the natural numbers,partial realizable maps
RT(K₂),sequences of natural numbers,partial realizable maps
Perm,the natural numbers,permutations
PDiff,piecewise-differentiable manifolds,piecewise-continuous maps
PL,piecewise-linear manifolds,piecewise-continuous maps
Prof,categories,profunctors
BiCat,bicategories,pseudofunctors
Rel,sets,relations
AdmRep,admissible domain representations,representable continuous maps
AbCat,Abelian categories,right exact functors
Rex,finitely cocomplete categories,right exact functors
CRing,commutative rings,ring maps
Ring,rings,ring maps
SRing,simplicial rings,ring maps
SemiGrp,semigroups,semigroup maps
SemiLat,semilattices,semilattice maps
SemiRing,semirings (rigs),semiring maps
BanRing,Banach rings,short group maps
CompNormGrp,complete normed groups,short group maps
NormGrp,normed groups,short group maps
NormRing,normed (commutative) rings,short group maps
BanAlg,Banach algebras,short linear maps
Ban_k,Banach spaces over fields k,short linear maps
FinHilb,finite-dimensional Hilbert spaces,short linear maps
Hilb,Hilbert spaces,short linear maps
CompMet,complete metric spaces,short maps
FinMet,finite metric spaces,short maps
LMet,Lawvere metric spaces,short maps
Met,metric spaces,short maps
PseudoMet,pseudometric spaces,short maps
SymLMet,symmetric Lawvere metric spaces,short maps
SSet,simplicial sets,simplicial maps
SimpCat,simplicially enriched categories,simplicially enriched functors
Aut,regular (Moore) automata,simulations
LieGrp,Lie groups,smooth group maps
CartSp,Cartesian spaces,smooth maps
Man,smooth manifolds,smooth maps
SMan,simplicial smooth manifolds,smooth maps
Span(Set),sets,spans of functions
Span(Grpd),groupoids,spans of tame functors
Spectra,topological spectra,spectrum 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
Quant,quantales,suplattice maps
SupLat,suplattices,suplattice maps
Surj,sets,surjections
SymmRel,sets,symmetric relations
Feyn,Feynman diagrams,symmetries of Feynman diagrams
2,two objects,the walking arrow (and two identity arrows)
I,two objects,the walking isomorphism (and two identity arrows)
Ω,the inhabited trees,tree maps
Hilb₀,Hilbert spaces,unitary operators
DagCat,†-categories (dagger categories),†-functors (dagger functors)