# categories

### 175 rows

This data as json, CSV (advanced)

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 |

### Advanced export

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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") );