Pith Number

pith:Y4MJW66X

pith:2024:Y4MJW66XCN27Y6FOF3UMVX7HUL

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Univalent Enriched Categories and the Enriched Rezk Completion

Niels van der Weide

Univalent enriched categories make every essentially surjective fully faithful functor an equivalence and admit a Rezk completion.

arxiv:2401.11752 v7 · 2024-01-22 · cs.LO · math.CT

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Claims

C1strongest claim

We prove that all essentially surjective and fully faithful functors between univalent enriched categories are equivalences, and we show that every enriched category admits a Rezk completion. Finally, we use the Rezk completion for enriched categories to construct univalent enriched Kleisli categories.

C2weakest assumption

The proofs rely on the ambient univalent foundations (homotopy type theory) in which equality of objects is given by paths and in which the base of enrichment satisfies the necessary univalence and completeness properties; if the enrichment category fails to be univalent or if the Rezk completion construction does not preserve the enrichment structure, the central claims would not hold.

C3one line summary

Proves that fully faithful essentially surjective functors are equivalences for univalent enriched categories, establishes existence of Rezk completion for any enriched category, and constructs univalent enriched Kleisli categories.

Receipt and verification

First computed	2026-06-02T03:05:03.138901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7189b7bd71375fc78ae2ee8cadfe7a2f3173bf92b683591f892aa0a23879dfc

Aliases

arxiv: 2401.11752 · arxiv_version: 2401.11752v7 · doi: 10.48550/arxiv.2401.11752 · pith_short_12: Y4MJW66XCN27 · pith_short_16: Y4MJW66XCN27Y6FO · pith_short_8: Y4MJW66X

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Y4MJW66XCN27Y6FOF3UMVX7HUL \
  | 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: c7189b7bd71375fc78ae2ee8cadfe7a2f3173bf92b683591f892aa0a23879dfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b7b7bac6f83f15b11d3769ed24023fce24bf8b43590b6601a47656a8059f90d",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2024-01-22T08:27:08Z",
    "title_canon_sha256": "ce91f42eed874178d9bb7c9a2e4f4d2fd1ddd63e6ada9796d022fa4cfe3ee7da"
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  "schema_version": "1.0",
  "source": {
    "id": "2401.11752",
    "kind": "arxiv",
    "version": 7
  }
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