Pith Number

pith:GZLXUTPE

pith:2025:GZLXUTPEJBWRAEF4RMFU3NEG4H

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Coherent and ideal actions in ideally exact categories

Federica Piazza, Giuseppe Metere, Manuel Mancini

Every ideal action is coherent in ideally exact categories, with the converse true in key contexts.

arxiv:2507.06124 v3 · 2025-07-08 · math.CT · math.LO · math.RA

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Claims

C1strongest claim

Every ideal action is coherent, and the converse holds in some relevant ideally exact contexts; a connection exists with Janelidze's semidirect product in ideally exact categories.

C2weakest assumption

The newly introduced definitions of internal coherent action and internal ideal action correctly generalize the intended aspects of unital actions of rings and algebras within the framework of ideally exact categories.

C3one line summary

Defines internal coherent and ideal actions in ideally exact categories, proves every ideal action is coherent with converse in some contexts, and analyzes links to Janelidze's semidirect products.

References

50 extracted · 50 resolved · 1 Pith anchors

[1] M. Abad, D. N. Castaño and J. P. Díaz Varela,MV-closures of Wajsberg hoops and applica- tions, Algebra Universalis64 (2010), 213–230 2010

[2] R. J. Adillon and V. Vérdu,On product logic, Soft Computing2 (1998), 141–146 1998

[3] P. Agliano, I. Ferreirim and F. Montagna,Basic Hoops: an Algebraic Study of Continuous t-norms, Studia Logica87 (2007), 73–98 2007

[4] M. Barr, P. A. Grillet and D. H. Osdol,Exact categories and categories of sheaves, Lecture Notes in Mathemathics236 (1971) 1971

[5] W. Blok, I. Ferreirim,On the structure of hoops, Algebra universalis43 (2000), 233–257 2000

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-25T02:02:07.880256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36577a4de4486d1010bc8b0b4db486e1fb9b10ba5b4a92678699b9abd1bfdb72

Aliases

arxiv: 2507.06124 · arxiv_version: 2507.06124v3 · doi: 10.48550/arxiv.2507.06124 · pith_short_12: GZLXUTPEJBWR · pith_short_16: GZLXUTPEJBWRAEF4 · pith_short_8: GZLXUTPE

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GZLXUTPEJBWRAEF4RMFU3NEG4H \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 36577a4de4486d1010bc8b0b4db486e1fb9b10ba5b4a92678699b9abd1bfdb72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "394977632420784b71d36cd40d67d633947afcd173bcf7c5482d06305473013e",
    "cross_cats_sorted": [
      "math.LO",
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-07-08T16:08:48Z",
    "title_canon_sha256": "52c696a71bab8247374d12dcc02c09cc5ef1b5c12d14ab3f3a4ee897797475e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.06124",
    "kind": "arxiv",
    "version": 3
  }
}