Publication details

Two-dimensional monadicity

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BOURKE John Denis

Year of publication 2014
Type Article in Periodical
Magazine / Source Advances in Mathematics
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords 2-category 2-monad F-category Weak morphism Monadicity
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Description 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.
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