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PreprintCC BY-SA 4.0arXiv

Bicategorical Idempotent Completion

  • Tessa Kammermeier
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Abstract

In recent years, higher categorical variants of idempotents have become an object of interest. Notably, they appear when categorifying algebraic structures motivated by mathematical physics. Working in the setting of bicategories, we give a rigorous definition of the bicategorical idempotent completion as outlined by Gaiotto and Johnson-Freyd in arXiv:1905.09566. We show that this agrees with the Cauchy completion of a locally idempotent complete bicategory in the sense of Lawvere.

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Cite

BibTeXRIS
BibTeX
@misc{kammermeier2026bicategorical,
  title = {{Bicategorical Idempotent Completion}},
  author = {Tessa Kammermeier},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13788},
  eprint = {2609.13788},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13788},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Bicategorical Idempotent Completion
AU  - Tessa Kammermeier
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.13788
UR  - https://arxiv.org/abs/2609.13788
AB  - In recent years, higher categorical variants of idempotents have become an object of interest. Notably, they appear when categorifying algebraic structures motivated by mathematical physics. Working in the setting of bicategories, we give a rigorous definition of the bicategorical idempotent completion as outlined by Gaiotto and Johnson-Freyd in arXiv:1905.09566. We show that this agrees with the Cauchy completion of a locally idempotent complete bicategory in the sense of Lawvere.
ER  -