Pith Number

pith:LV22X6ZN

pith:2025:LV22X6ZNTHRCSBZQE2YVMVAS4P

not attested not anchored not stored refs pending

On the equivalence between the existence of $n$-kernels and $n$-cokernels

Vitor Gulisz, Wolfgang Rump

In idempotent complete preadditive categories with weak kernels and weak cokernels, n-kernels exist exactly when n-cokernels do.

arxiv:2510.23369 v2 · 2025-10-27 · math.CT · math.RA · math.RT

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\usepackage{pith}
\pithnumber{LV22X6ZNTHRCSBZQE2YVMVAS4P}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

If an idempotent complete preadditive category has weak kernels and weak cokernels, then it has n-kernels if and only if it has n-cokernels, where n is a nonnegative integer.

C2weakest assumption

The category under consideration is idempotent complete and preadditive and already possesses weak kernels and weak cokernels (as stated in the main theorem).

C3one line summary

In idempotent complete preadditive categories with weak kernels and weak cokernels, n-kernels exist if and only if n-cokernels exist.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-25T02:01:08.918222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d75abfb2d99e229073026b1565412e3fafb07b89cfc85171239ce2089a9e883

Aliases

arxiv: 2510.23369 · arxiv_version: 2510.23369v2 · doi: 10.48550/arxiv.2510.23369 · pith_short_12: LV22X6ZNTHRC · pith_short_16: LV22X6ZNTHRCSBZQ · pith_short_8: LV22X6ZN

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LV22X6ZNTHRCSBZQE2YVMVAS4P \
  | 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: 5d75abfb2d99e229073026b1565412e3fafb07b89cfc85171239ce2089a9e883

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9cbf9c7df81c4c8094cdd633f1cbc61bce915bf34ef3a947c1138adf443fe7b7",
    "cross_cats_sorted": [
      "math.RA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-10-27T14:20:01Z",
    "title_canon_sha256": "57f1df92f029739eefe31eea65ebc53a2cdb42e2d93de6266b3d902b4fb04adc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.23369",
    "kind": "arxiv",
    "version": 2
  }
}