Pith Number

pith:D3Y3LJVG

pith:2026:D3Y3LJVGQHDE2GNZ4LYXEAA4CZ

not attested not anchored not stored refs pending

Enhanced $2$-categories of models of sketches as enhanced $2$-categories of algebras over monads

Joanna Ko

Models of any enhanced limit 2-sketch with tight cones are equivalent to algebras over an enhanced 2-monad.

arxiv:2605.04516 v2 · 2026-05-06 · math.CT

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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 any enhanced limit 2-sketch T with tight cones, the enhanced 2-category Mod_{s,w}(T, K) of models in a locally presentable enhanced 2-category K is equivalent to the enhanced 2-category T-Alg_{s,w} of algebras over an enhanced 2-monad T on Mod(T_τ, K), including tight and loose w-morphisms.

C2weakest assumption

That K is locally presentable as an enhanced 2-category and that the sketch T has tight cones; the monadicity and limit characterizations rest on the base of enrichment being locally presentable and on the enriched Orthogonal Subcategory Theorem holding in this setting.

C3one line summary

Models of enhanced limit 2-sketches are equivalent to algebras over enhanced 2-monads, including lax morphisms, and inherit w-rigged limits.

Receipt and verification

First computed	2026-05-28T01:04:41.600746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ef1b5a6a681c64d19b9e2f172001c1646feb828f54f0cbeccfcdf0d7c732d9e

Aliases

arxiv: 2605.04516 · arxiv_version: 2605.04516v2 · doi: 10.48550/arxiv.2605.04516 · pith_short_12: D3Y3LJVGQHDE · pith_short_16: D3Y3LJVGQHDE2GNZ · pith_short_8: D3Y3LJVG

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/D3Y3LJVGQHDE2GNZ4LYXEAA4CZ \
  | 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: 1ef1b5a6a681c64d19b9e2f172001c1646feb828f54f0cbeccfcdf0d7c732d9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0e1fdec38d318fbb46304420bad18df060708db48ffd5faca085800ef3f80e6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-05-06T05:49:02Z",
    "title_canon_sha256": "7f109ed5594a1781fd365664b08e8113311a9c47d1fb6845070c7879143987a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04516",
    "kind": "arxiv",
    "version": 2
  }
}