categories
175 rows sorted by name descending
This data as json, CSV (advanced)
name ▲ | objects_hr | arrows_hr |
---|---|---|
□ | 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) |
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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") );