Codescent and Bicolimits of Pseudo-Algebras

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 th...

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Veröffentlicht in:	Applied categorical structures 2024, Vol.32 (2)
1. Verfasser:	Osmond, Axel
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Sprache:	eng
Schlagworte:	Algebra Convex and Discrete Geometry Existence theorems Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Theory of Computation
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description	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.
doi_str_mv	10.1007/s10485-024-09765-0
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title	Codescent and Bicolimits of Pseudo-Algebras
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