Pith Number

pith:2XF56672

pith:2026:2XF56672SVMPP4JE4THVYTB6TK

not attested not anchored not stored refs pending

Presheaves and cocompletions in formal category theory

Dylan McDermott, Nathanael Arkor

In virtual equipments satisfying mild assumptions, presheaf constructions exhibit free cocompletions under classes of weights.

arxiv:2604.22370 v2 · 2026-04-24 · math.CT

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\usepackage{pith}
\pithnumber{2XF56672SVMPP4JE4THVYTB6TK}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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

We show that, in a virtual equipment satisfying mild assumptions, free cocompletions under classes of weights are exhibited by presheaf constructions.

C2weakest assumption

The virtual equipment satisfies mild assumptions (not specified in detail in the abstract) that allow presheaf constructions to exhibit free cocompletions and the extension of weighted colimits.

C3one line summary

In virtual equipments with mild assumptions, presheaf constructions provide free cocompletions under classes of weights, extending weighted colimits and enabling constructions for enriched categories in monoidal categories and bicategories.

Receipt and verification

First computed	2026-07-28T02:23:30.954513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5cbdf7bfa9558f7f124e4cf5c4c3e9a8c0a13d6d852b6594981286655f64825

Aliases

arxiv: 2604.22370 · arxiv_version: 2604.22370v2 · doi: 10.48550/arxiv.2604.22370 · pith_short_12: 2XF56672SVMP · pith_short_16: 2XF56672SVMPP4JE · pith_short_8: 2XF56672

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2XF56672SVMPP4JE4THVYTB6TK \
  | 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: d5cbdf7bfa9558f7f124e4cf5c4c3e9a8c0a13d6d852b6594981286655f64825

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d47a03f368e9dcfbb564ba42757c05667c34d7515b27e614df41ecefb9716729",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-04-24T09:02:20Z",
    "title_canon_sha256": "4f91e134b763df988af0121cddea33a272ae16ebda6f7e3e58f7fa2373d0008e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.22370",
    "kind": "arxiv",
    "version": 2
  }
}