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