1 |
(is) the point |
(is) the identity arrow |
2Cat |
2-categories |
2-functors |
Circ |
the natural numbers |
Boolean circuits |
Poiss |
smooth manifolds with Poisson structures |
Poisson maps |
DCPO |
directed-complete partial orders |
Scott-continuous maps |
CPO |
complete partial orders |
Scott-continuous maps |
R+ |
non-negative real numbers |
addition |
Alg(Ab) |
algebras of monoids in Ab (rings) |
algebra maps |
CommAlg(Ab) |
commutative algebras of monoids in Ab (rings) |
algebra maps |
Top* |
pointed topological spaces |
based continuous maps |
Set* |
pointed sets |
based maps |
Bij |
sets |
bijections |
Bimod(Ab) |
monoids in Ab (rings) |
bimodules of monoids in Ab (rings) |
CW |
CW complexes |
cellular maps |
SES(Ab) |
short exact sequences of Abelian groups |
commuting diagrams |
Mono |
injections |
commuting squares |
Sierp |
maps |
commuting squares |
EffAdmRep |
effective admissible domain representations |
computable continuous maps |
Eff |
sets with computable equality |
computable maps |
Ass |
assemblies |
computable maps |
KV |
computable real numbers |
computable maps |
TopCat |
topologically enriched categories |
continuous functors |
TopGrp |
topological groups |
continuous group maps |
STopGrp |
simplicial topological groups |
continuous group maps |
Comp |
compacta (compact Hausdorff spaces) |
continuous maps |
Diff |
differentiable manifolds |
continuous maps |
Loc |
locales |
continuous maps |
Top |
topological spaces |
continuous maps |
TopMan |
topological manifolds |
continuous maps |
Haus |
Hausdorff (T₂) spaces |
continuous maps |
Tych |
Tychonoff spaces |
continuous maps |
Stone |
Stone spaces |
continuous maps |
STop |
simplicial topological spaces |
continuous maps |
SoberTop |
sober topological spaces |
continuous maps |
SpLoc |
spatial locales |
continuous maps |
Ste |
stereotype spaces |
continuous maps |
1Type |
homotopy 1-types |
continuous maps |
TopMon |
topological monoids |
continuous monoid maps |
TopRing |
topological rings |
continuous ring maps |
AdicRing |
adic rings |
continuous ring maps |
AdicCRing |
commutative adic rings |
continuous ring maps |
□ |
the inhabited cubes |
cubical maps |
DSet |
dendroidal sets |
dendroidal maps |
DGCAlg |
differential-graded commutative algebras of vector spaces |
differential-graded algebra maps |
DGph |
digraphs |
digraph maps |
DblCat |
double categories |
double functors |
PROP |
monoidal product & permutation categories |
eso strict monoidal functors |
CPROP |
colored monoidal product & permutation categories |
eso strict monoidal functors |
Field |
fields |
field maps |
FinSet |
finite sets |
finite maps |
Frm |
frames |
frame maps |
Cat |
categories |
functors |
Grpd |
groupoids |
functors |
RCat |
restriction categories |
functors |
Topos |
topoi |
geometric arrows |
G |
the natural numbers |
globe maps |
DirGph |
directed graphs |
graph maps |
Gph |
undirected graphs |
graph maps |
Quiv |
quivers |
graph maps |
Ab |
Abelian groups |
group maps |
FinGrp |
finite groups |
group maps |
Grp |
groups |
group maps |
NormAb |
normed Abelian groups |
group maps |
Tor |
Torsion groups |
group maps |
AbTor |
Abelian torsion groups |
group maps |
AbTorF |
torsion-free Abelian groups |
group maps |
SGrp |
simplicial groups |
group maps |
SAb |
simplicial Abelian groups |
group maps |
LieRing |
Lie rings |
group maps |
Ho(Eff) |
numbered sets |
homotopy classes of computable maps |
Ho(Top) |
topological spaces |
homotopy classes of continuous maps |
Hyp |
finite directed hypergraphs |
hypergraph maps |
Idem |
idempotent endofunctions |
idempotency-respecting maps |
Op(FinCartSp) |
open sets of finite-dimensional Cartesian spaces |
inclusions |
Inj |
sets |
injections |
BoolAlg |
Boolean algebras |
lattice maps |
CompBoolAlg |
complete Boolean algebras (CABAs) |
lattice maps |
CompLat |
complete lattices |
lattice maps |
DistLat |
distributive lattices |
lattice maps |
HeytAlg |
Heyting algebras |
lattice maps |
Lat |
lattices |
lattice maps |
MonCat |
monoidal categories |
lax monoidal functors |
SymCat |
symmetric monoidal categories |
lax monoidal functors |
BrMonCat |
braided monoidal categories |
lax monoidal functors |
SymmMonCat |
symmetric monoidal categories |
lax monoidal functors |
TracedSymmMonCat |
traced symmetric monoidal categories |
lax monoidal functors |
CompCat |
compact closed categories |
lax monoidal functors |
*Aut |
star-autonomous categories |
lax monoidal functors |
DagCompCat |
compact closed †-categories |
lax monoidal †-functors |
PrCat |
locally presentable categories |
left adjoint functors |
Lex |
finitely complete categories |
left exact functors |
Ch.(Vect_k) |
chain complices of vector spaces |
linear maps |
FinVect_k |
finite vector spaces over fields k |
linear maps |
Vect_k |
vector spaces over fields k |
linear maps |
TopVect |
topological vector spaces |
linear maps |
LieAlg_k |
Lie algebras over vector spaces over fields k |
linear maps |
SLieAlg_k |
simplicial Lie algebras over vector spaces over fields k |
linear maps |
FinVect_q |
finite vector spaces over finite fields of order q |
linear maps |
Log |
topoi |
logical functors |
Set |
sets |
maps |
Mat_k |
the natural numbers |
matrices over fields k |