Pith Number

pith:ITFOVIKA

pith:2026:ITFOVIKAIFGG7M57JNXOMX5ASR

not attested not anchored not stored refs resolved

Fat Lie Theory

Lennart Obster

Fat extensions of Lie groupoids correspond one-to-one with abstract 2-term representations up to homotopy.

arxiv:2603.08176 v2 · 2026-03-09 · math.DG · math.AT · math.RT · math.SG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ITFOVIKAIFGG7M57JNXOMX5ASR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

We obtain a one-to-one correspondence between [the category of fat extensions and the category of abstract 2-term representations up to homotopy], and relate to the well-known equivalence between 2-term ruths and VB-groupoids/algebroids. [...] we upgrade the one-to-one correspondence between general linear PB-groupoids and VB-groupoids of Cattafi and Garmendia to an equivalence of categories.

C2weakest assumption

The newly defined categories of fat extensions and abstract 2-term ruths are well-posed and the stated one-to-one correspondences and equivalences hold under the standard assumptions of Lie groupoid theory without hidden restrictions on the objects involved.

C3one line summary

Fat Lie theory defines fat extensions and abstract 2-term ruths with one-to-one correspondences to general linear PB-groupoids and core-transitive double groupoids, upgrading prior equivalences to category equivalences.

References

14 extracted · 14 resolved · 3 Pith anchors

[1] [CdH26] A. Cabrera and M. L. del Hoyo. Geometric differentiation of simplicial manifolds. Preprint, arXiv:2602.09885 [math.DG],

[2] [CF05] M. Crainic and R. L. Fernandes. Secondary characteristic classes of Lie algebroids. InQuantum field theory and noncommutative geometry. Based on the workshop, Sendai, Japan, November 2002, page 2002

[3] [CMS20] M. Crainic, J. N. Mestre, and I. Struchiner. Deformations of Lie groupoids.Int. Math. Res. Not., 2020(21):7662–7746, 2020

[4] Carrillo Rouse 2006

[5] arXiv preprint math/0403266 (2004) · arXiv:math/0403266

Receipt and verification

First computed	2026-05-17T23:38:59.697742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44caeaa140414c6fb3bf4b6ee65fa0945aec9a9b26a5b00b6fa41413771c790e

Aliases

arxiv: 2603.08176 · arxiv_version: 2603.08176v2 · doi: 10.48550/arxiv.2603.08176 · pith_short_12: ITFOVIKAIFGG · pith_short_16: ITFOVIKAIFGG7M57 · pith_short_8: ITFOVIKA

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/ITFOVIKAIFGG7M57JNXOMX5ASR \
  | 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: 44caeaa140414c6fb3bf4b6ee65fa0945aec9a9b26a5b00b6fa41413771c790e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a758640080aa3354cf2ee1f9129f16c1768c8c3c6dc9755ec4e7f797d8738d8",
    "cross_cats_sorted": [
      "math.AT",
      "math.RT",
      "math.SG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-03-09T09:57:03Z",
    "title_canon_sha256": "b5bc9cdad4a70dce8a06834dffe9f6345bc4b39f3288de29c3eb793330ede93c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.08176",
    "kind": "arxiv",
    "version": 2
  }
}