Two-dimensional monadicity

John Bourke*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


The behaviour of limits of weak morphisms in 2-dimensional universal algebra is not 2-categorical in that, to fully express the behaviour that occurs, one needs to be able to quantify over strict morphisms amongst the weaker kinds. F-categories were introduced to express this interplay between strict and weak morphisms. We express doctrinal adjunction as an F-categorical lifting property and use this to give monadicity theorems, expressed using the language of F-categories, that cover each weaker kind of morphism.

Original languageEnglish
Pages (from-to)708-747
Number of pages40
JournalAdvances in Mathematics
Publication statusPublished - 15 Feb 2014
Externally publishedYes


  • 2-category
  • 2-monad
  • F-category
  • Monadicity
  • Primary
  • Weak morphism


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