Abstract
We categorify cocompleteness results of monad theory, in the context of pseudomonads. We first prove a general result establishing that, in any 2-category, weighted bicolimits can be constructed from oplax bicolimits and bicoequalizers of codescent objects. After prerequisites on pseudomonads and their pseudo-algebras, we give a 2-dimensional Linton theorem reducing bicocompleteness of 2-categories of pseudo-algebras to existence of bicoequalizers of codescent objects. Finally we prove this condition to be fulfilled in the case of a bifinitary pseudomonad, ensuring bicocompleteness.
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The author acknowledges the support of the Grothendieck Institute through his post-doctoral fellowship inside the project Topos theory and its applications.
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Axel Osmond is the author of this paper.
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Communicated by Nicola Gambino.
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Osmond, A. Codescent and Bicolimits of Pseudo-Algebras. Appl Categor Struct 32, 11 (2024). https://doi.org/10.1007/s10485-024-09765-0
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DOI: https://doi.org/10.1007/s10485-024-09765-0
Keywords
- Codescent
- Bicolimits
- Pseudo-algebras
- Pseudomonad
- Bifinitary
- Transfinite induction
- Bicoequalizer of codescent object