| *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 |