Pith Number

pith:YMP4LKXY

pith:2026:YMP4LKXYRJGSZIJ453VMLH2ILF

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Implementing the biset category of finite groups

Fabian Zickgraf, Marc Talleux, Mohamed Barakat

The biset category of finite groups is implemented as a tower of standard categorical constructions in the CAP software.

arxiv:2604.18346 v2 · 2026-04-20 · math.CT · math.GR

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Claims

C1strongest claim

We describe an implementation of the biset category of finite groups as a tower of standard categorical constructions, all of which are implemented in the software project CAP for algorithmic category theory. In particular, we describe the composition of bisets as a composition in a Kleisli category of some biadjunction monad. This composition relies on the universal property of the coequalizer completion of a group viewed as a groupoid on one object. Implementing this universal property makes nontrivial use of the Schreier-Sims orbit algorithm.

C2weakest assumption

That the universal property of the coequalizer completion of a one-object groupoid can be realized algorithmically via the Schreier-Sims orbit algorithm in a manner that correctly implements biset composition inside the existing CAP framework.

C3one line summary

Implementation of the biset category of finite groups in CAP as a tower of categorical constructions, with biset composition realized as Kleisli composition of a biadjunction monad using the Schreier-Sims algorithm on coequalizer completions.

Receipt and verification

First computed	2026-05-21T02:05:03.142930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c31fc5aaf88a4d2ca13ceeeac59f485974d7e97630a1e862b181735d2812c4ed

Aliases

arxiv: 2604.18346 · arxiv_version: 2604.18346v2 · doi: 10.48550/arxiv.2604.18346 · pith_short_12: YMP4LKXYRJGS · pith_short_16: YMP4LKXYRJGSZIJ4 · pith_short_8: YMP4LKXY

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YMP4LKXYRJGSZIJ453VMLH2ILF \
  | 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: c31fc5aaf88a4d2ca13ceeeac59f485974d7e97630a1e862b181735d2812c4ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "336e15afc8f78bd3afd9a63a6267e424b186fecd57f8dc7adf48019565aa2e00",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-04-20T14:42:12Z",
    "title_canon_sha256": "6a4570da804ee275be570e8cde7c3a0bb7df57b968f48d8c26964a6461516c07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.18346",
    "kind": "arxiv",
    "version": 2
  }
}