categories
175 rows sorted by arrows_hr descending
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name | objects_hr | arrows_hr ▲ |
---|---|---|
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 |
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CREATE TABLE "categories" ( "name" TEXT NOT NULL UNIQUE, "objects_hr" TEXT NOT NULL, "arrows_hr" TEXT NOT NULL, PRIMARY KEY("name") );