2022/04/12 by Osmond, Axel
#Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2204.06055
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.