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