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PreprintarXiv licencearXiv

Cocompletion under sifted colimits need not be finitely accessible

  • Yuto Kawase
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Abstract

We give a negative answer to the open problem posed by Adámek and Rosický in 2001, asking whether the cocompletion of any small category under sifted colimits is finitely accessible. We will construct an infinite family of counterexamples.

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Cite

BibTeXRIS
BibTeX
@misc{kawase2026cocompletion,
  title = {{Cocompletion under sifted colimits need not be finitely accessible}},
  author = {Yuto Kawase},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08548},
  eprint = {2610.08548},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08548},
}
RIS
TY  - UNPB
TI  - Cocompletion under sifted colimits need not be finitely accessible
AU  - Yuto Kawase
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08548
UR  - https://arxiv.org/abs/2610.08548
AB  - We give a negative answer to the open problem posed by Adámek and Rosický in 2001, asking whether the cocompletion of any small category under sifted colimits is finitely accessible. We will construct an infinite family of counterexamples.
ER  -