Pith Number

pith:AGIOFYJ2

pith:2026:AGIOFYJ2BMGSLBRUTDEX6B26DE

not attested not anchored not stored refs resolved

Revising Auslander-Gruson-Jensen duality

Jiaqun Wei, Ramin Ebrahimi, Rasool Hafezi

A simple description of the free abelian category clarifies Auslander-Gruson-Jensen duality for modules over a ring.

arxiv:2605.03458 v2 · 2026-05-05 · math.RT · math.CT · math.RA

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

we give a simple description of the free abelian category. This description clarifies Auslander-Gruson-Jensen duality and also the duality between definable subcategories of right A-modules and those of left A-modules.

C2weakest assumption

The existence of this duality arises from the fact that mod-(mod-A) is the free abelian category over the pre-additive category A with a single object.

C3one line summary

Gives a simple description of the free abelian category to clarify Auslander-Gruson-Jensen duality between definable subcategories of right and left modules over a ring.

References

12 extracted · 12 resolved · 0 Pith anchors

[1] Abelian categories over additive ones 1973

[2] Coherent functors 1965

[3] Isolated singularities and existence of almost split sequences 1984

[4] When are definable classes tilting and cotilting classes? 2008

[5] On definable subcategories 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:40.575985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0190e2e13a0b0d25863498c97f075e1908e349b835596ab6c670ed5def5259b1

Aliases

arxiv: 2605.03458 · arxiv_version: 2605.03458v2 · doi: 10.48550/arxiv.2605.03458 · pith_short_12: AGIOFYJ2BMGS · pith_short_16: AGIOFYJ2BMGSLBRU · pith_short_8: AGIOFYJ2

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/AGIOFYJ2BMGSLBRUTDEX6B26DE \
  | 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: 0190e2e13a0b0d25863498c97f075e1908e349b835596ab6c670ed5def5259b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96718a625bcaf4f2fc3916869b93724e7f045af02fa3367a838388ad69051575",
    "cross_cats_sorted": [
      "math.CT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-05-05T07:45:24Z",
    "title_canon_sha256": "bb7d0121d16aecdcab160e9f3de5c4a2fb2ad33ea0311f3552c334d1a208d328"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03458",
    "kind": "arxiv",
    "version": 2
  }
}