Pith Number

pith:JYME25CG

pith:2026:JYME25CGMXUO2I7F2UM2UHENOF

not attested not anchored not stored refs resolved

Sphericalization and the Universal Spherical Adjunction

Fernando Abell\'an, Jonte G\"odicke

Any adjunction of stable infinity-categories can be turned into a spherical adjunction by inverting its twist and cotwist functors.

arxiv:2605.15037 v1 · 2026-05-14 · math.CT · math.AT · math.RT

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4 Citations open

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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

For every adjunction of stable ∞-categories we give a simple procedure for inverting the twist and cotwist functors; this yields an explicit left and right adjoint to the inclusion of the (∞,2)-category of spherical adjunctions into all adjunctions, plus a description of the walking spherical adjunction.

C2weakest assumption

The ambient structure is a locally stable (∞,2)-category in which the given adjunction lives and in which the twist and cotwist functors are well-defined and invertible after the procedure.

C3one line summary

A construction inverts twists in adjunctions of stable infinity-categories, producing adjoints to the spherical adjunction inclusion and a walking spherical adjunction that classifies them.

References

74 extracted · 74 resolved · 2 Pith anchors

[1] Justin Hilburn , title =

[2] Fully faithful functors and pushouts of -categories , author=. 2025 , eprint= 2025

[3] Spectral Algebraic Geometry , author=

[4] Free fibrations, lax colimits and

[5] ( ,2) -Topoi and descent , author=. 2024 , eprint= 2024

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:38:54.525058Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e184d744665e8ed23e5d519aa1c8d716be7ac33b3c7b20d764cd4ab155ec231

Aliases

arxiv: 2605.15037 · arxiv_version: 2605.15037v1 · doi: 10.48550/arxiv.2605.15037 · pith_short_12: JYME25CGMXUO · pith_short_16: JYME25CGMXUO2I7F · pith_short_8: JYME25CG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JYME25CGMXUO2I7F2UM2UHENOF \
  | 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: 4e184d744665e8ed23e5d519aa1c8d716be7ac33b3c7b20d764cd4ab155ec231

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa62330116df0169bf67acac3f809cc3d90c724aeba066adf423f84b208f904d",
    "cross_cats_sorted": [
      "math.AT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-05-14T16:30:52Z",
    "title_canon_sha256": "4cf588fdfb05cf1fca8db7237e782e586ddbd7d7ace09d73c297275bf1381e28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15037",
    "kind": "arxiv",
    "version": 1
  }
}