Pith Number

pith:XLGC5Z5H

pith:2025:XLGC5Z5HJ4MF5JQVHEWZM7I56Z

not attested not anchored not stored refs pending

Double categories of profunctors

Yuto Kawase

Virtual double categories of enriched categories, functors, and profunctors are characterized by a new notion of double-categorical colimits.

arxiv:2504.11099 v4 · 2025-04-15 · math.CT

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\usepackage{pith}
\pithnumber{XLGC5Z5HJ4MF5JQVHEWZM7I56Z}

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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 characterize virtual double categories of enriched categories, functors, and profunctors by introducing a new notion of double-categorical colimits. Our characterization is strict in the sense that it is up to equivalence between virtual double categories and, at the level of objects, up to isomorphism of enriched categories.

C2weakest assumption

The choice to treat enrichment in a unital virtual double category rather than in a bicategory or a monoidal category, together with the adoption of augmented virtual double categories as the fundamental language for double-categorical concepts.

C3one line summary

Characterizes virtual double categories of enriched categories, functors, and profunctors via a new notion of double-categorical colimits, strictly up to equivalence.

Cited by

1 paper in Pith

The familial nature of enrichment over virtual double categories

Receipt and verification

First computed	2026-06-10T01:09:16.265272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bacc2ee7a74f185ea615392d967d1df65a611493558cfaef4c85f4f2a1efbf7f

Aliases

arxiv: 2504.11099 · arxiv_version: 2504.11099v4 · doi: 10.48550/arxiv.2504.11099 · pith_short_12: XLGC5Z5HJ4MF · pith_short_16: XLGC5Z5HJ4MF5JQV · pith_short_8: XLGC5Z5H

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/XLGC5Z5HJ4MF5JQVHEWZM7I56Z \
  | 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: bacc2ee7a74f185ea615392d967d1df65a611493558cfaef4c85f4f2a1efbf7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e95bdcb30962d8ade48e391159603dbc3182f4909ca62de52e3de098769d725",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-04-15T11:45:59Z",
    "title_canon_sha256": "95f1f76239b4b8261d9efda7db177386df65a179008c1029af2dd322497a5159"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.11099",
    "kind": "arxiv",
    "version": 4
  }
}