□ |
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 |