categories

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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")
);