Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 14 min ago
PreprintCC0arXiv

On the enriched approximate completeness

  • Boris Chorny
  • Giuseppe Leoncini
Open at sourcePDFDOICite

Abstract

We generalize to the enriched setting the classical theorem of Freyd, that the free cocompletion ๐’ซA of a category ๐’œ is complete if and only if ๐’œ is approximately complete. The work of Day and Lack, arXiv:math/0610439, has laid the foundations for such a generalization and has had multiple applications in homotopy theory and in category theory. Our result allows us to expand on some of these applications.

Related

  1. Weak Polynomial Completeness Does Not Imply Almost Polynomial Completeness
    Viet-Hoang Tran, Tan N. Nguyen
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Counterexamples to the Monotone Completeness Conjecture
    Jananan Arulseelan, James E. Hanson
    arXivPreprintarXiv licenceFull textAnalysis & PDEsLogic & foundationsarXiv
  3. A two-dimensional counterexample for Kobayashi completeness of balanced domains
    Armen Edigarian
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  4. Friedman--Stanley cofinality without Borel completeness
    Ruijun Wang
    arXivPreprintCC BY 4.0Full textLogic & foundationsarXiv
  5. Completeness of constructible norms
    Juan Rafael Acosta-Portilla, Armando Sรกnchez-Nungaray, Gerardo Ramos-Vรกzquez +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{chorny2026enriched,
  title = {{On the enriched approximate completeness}},
  author = {Boris Chorny and Giuseppe Leoncini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33543},
  eprint = {2610.33543},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33543},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - On the enriched approximate completeness
AU  - Boris Chorny
AU  - Giuseppe Leoncini
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33543
UR  - https://arxiv.org/abs/2610.33543
AB  - We generalize to the enriched setting the classical theorem of Freyd, that the free cocompletion ๐’ซA of a category ๐’œ is complete if and only if ๐’œ is approximately complete. The work of Day and Lack, arXiv:math/0610439, has laid the foundations for such a generalization and has had multiple applications in homotopy theory and in category theory. Our result allows us to expand on some of these applications.
ER  -