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arXiv · 2204.06055

Codescent and bicolimits of pseudo-algebras

Axel Osmond
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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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Axel Osmond. 2022-04-12. Codescent and bicolimits of pseudo-algebras. https://arxiv.org/abs/2204.06055

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