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finite monoid karoubi envelope
For a fully captured associative monoid multiplication table on1..4 original labels0..n-1 with identity0, reconstruct its WHOLE Karoubi envelope. table[x][y] means x*y, no commutativity assumed. objects are EVERY idempotent e with e*e=e, ascending and retained separately even if isomorphic. arrows are ALL triples[source_e,target_f,m] satisfying f*m=m=m*e, numeric lexicographic order. This OWN triple order differs from literature(e,m,f). identities[i] is the arrow.
POST https://datenvertrag.halowerk.com/v1/finite-monoid-karoubi-envelopeEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| table | Siehe Schema | Ja | |
| claim | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"properties": {
"table": {
"anyOf": [
{
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 1,
"maxItems": 4
},
"minItems": 1,
"maxItems": 4
},
{
"type": "null"
}
]
},
"claim": {
"anyOf": [
{
"type": "object",
"properties": {
"objects": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 1,
"maxItems": 4
},
"arrows": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 3,
"maxItems": 3
},
"minItems": 1,
"maxItems": 64
},
"identities": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 63
},
"minItems": 1,
"maxItems": 4
},
"composition": {
"type": "array",
"items": {
"type": "array",
"items": {
"anyOf": [
{
"type": "integer",
"minimum": 0,
"maximum": 63
},
{
"type": "null"
}
]
},
"minItems": 1,
"maxItems": 64
},
"minItems": 1,
"maxItems": 64
}
},
"required": [
"objects",
"arrows",
"identities",
"composition"
],
"additionalProperties": false
},
{
"type": "null"
}
]
}
},
"required": [
"table",
"claim"
],
"additionalProperties": false
}Veröffentlichtes Eingabebeispiel
{
"table": [
[
0
]
],
"claim": {
"objects": [
0
],
"arrows": [
[
0,
0,
0
]
],
"identities": [
0
],
"composition": [
[
0
]
]
}
}Ergebnis & Dokumentation
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Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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