categories
175 rows
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| name ▼ | objects_hr | arrows_hr |
|---|---|---|
| *Aut | star-autonomous categories | lax monoidal functors |
| 1 | (is) the point | (is) the identity arrow |
| 1Type | homotopy 1-types | continuous maps |
| 2 | two objects | the walking arrow (and two identity arrows) |
| 2Cat | 2-categories | 2-functors |
| Ab | Abelian groups | group maps |
| AbCat | Abelian categories | right exact functors |
| AbTor | Abelian torsion groups | group maps |
| AbTorF | torsion-free Abelian groups | group maps |
| AdicCRing | commutative adic rings | continuous ring maps |
| AdicRing | adic rings | continuous ring maps |
| AdmRep | admissible domain representations | representable continuous maps |
| Alg(Ab) | algebras of monoids in Ab (rings) | algebra maps |
| Ass | assemblies | computable maps |
| Aut | regular (Moore) automata | simulations |
| BanAlg | Banach algebras | short linear maps |
| BanRing | Banach rings | short group maps |
| Ban_k | Banach spaces over fields k | short linear maps |
| BiCat | bicategories | pseudofunctors |
| Bij | sets | bijections |
| Bimod(Ab) | monoids in Ab (rings) | bimodules of monoids in Ab (rings) |
| BoolAlg | Boolean algebras | lattice maps |
| BrMonCat | braided monoidal categories | lax monoidal functors |
| CMon | commutative monoids | monoid maps |
| CPO | complete partial orders | Scott-continuous maps |
| CPROP | colored monoidal product & permutation categories | eso strict monoidal functors |
| CRing | commutative rings | ring maps |
| CW | CW complexes | cellular maps |
| CartSp | Cartesian spaces | smooth maps |
| Cat | categories | functors |
| Ch.(Vect_k) | chain complices of vector spaces | linear maps |
| Circ | the natural numbers | Boolean circuits |
| Cluster | partitioned sets | non-refinement-increasing maps |
| CommAlg(Ab) | commutative algebras of monoids in Ab (rings) | algebra maps |
| Comp | compacta (compact Hausdorff spaces) | continuous maps |
| CompBoolAlg | complete Boolean algebras (CABAs) | lattice maps |
| CompCat | compact closed categories | lax monoidal functors |
| CompLat | complete lattices | lattice maps |
| CompMet | complete metric spaces | short maps |
| CompNormGrp | complete normed groups | short group maps |
| DCPO | directed-complete partial orders | Scott-continuous maps |
| DGCAlg | differential-graded commutative algebras of vector spaces | differential-graded algebra maps |
| DGph | digraphs | digraph maps |
| DSet | dendroidal sets | dendroidal maps |
| DagCat | †-categories (dagger categories) | †-functors (dagger functors) |
| DagCompCat | compact closed †-categories | lax monoidal †-functors |
| DblCat | double categories | double functors |
| Diff | differentiable manifolds | continuous maps |
| DirGph | directed graphs | graph maps |
| DistLat | distributive lattices | lattice maps |
| Eff | sets with computable equality | computable maps |
| EffAdmRep | effective admissible domain representations | computable continuous maps |
| Feyn | Feynman diagrams | symmetries of Feynman diagrams |
| Field | fields | field maps |
| FinGrp | finite groups | group maps |
| FinHilb | finite-dimensional Hilbert spaces | short linear maps |
| FinMet | finite metric spaces | short maps |
| FinOrd | the finite ordinal numbers | order-preserving maps |
| FinSet | finite sets | finite maps |
| FinVect_k | finite vector spaces over fields k | linear maps |
| FinVect_q | finite vector spaces over finite fields of order q | linear maps |
| Frm | frames | frame maps |
| G | the natural numbers | globe maps |
| Gph | undirected graphs | graph maps |
| Grp | groups | group maps |
| Grpd | groupoids | functors |
| Haus | Hausdorff (T₂) spaces | continuous maps |
| HeytAlg | Heyting algebras | lattice maps |
| Hilb | Hilbert spaces | short linear maps |
| Hilb₀ | Hilbert spaces | unitary operators |
| Ho(Cat) | categories | natural isomorphism classes of functors |
| Ho(Eff) | numbered sets | homotopy classes of computable maps |
| Ho(Grpd) | groupoids | natural isomorphism classes of functors |
| Ho(Top) | topological spaces | homotopy classes of continuous maps |
| Hyp | finite directed hypergraphs | hypergraph maps |
| I | two objects | the walking isomorphism (and two identity arrows) |
| Idem | idempotent endofunctions | idempotency-respecting maps |
| Inj | sets | injections |
| KV | computable real numbers | computable maps |
| LMet | Lawvere metric spaces | short maps |
| Lat | lattices | lattice maps |
| Lex | finitely complete categories | left exact functors |
| LieAlg_k | Lie algebras over vector spaces over fields k | linear maps |
| LieGrp | Lie groups | smooth group maps |
| LieRing | Lie rings | group maps |
| Loc | locales | continuous maps |
| Log | topoi | logical functors |
| Man | smooth manifolds | smooth maps |
| Mat_R | the natural numbers | matrices over rings R |
| Mat_SR | the natural numbers | matrices over semirings SR |
| Mat_k | the natural numbers | matrices over fields k |
| Meas | measurable spaces | measurable maps |
| Met | metric spaces | short maps |
| Mod(Ab) | modules of monoids in Ab (rings) | module maps |
| Mon | monoids | monoid maps |
| MonCat | monoidal categories | lax monoidal functors |
| Mono | injections | commuting squares |
| MultiSet | multisets | multimaps |
| NormAb | normed Abelian groups | group maps |
| NormGrp | normed groups | short group 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")
);