Two-dimensional monadicity
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Periodical |
| Magazine / Source | Advances in Mathematics |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.aim.2013.11.007 |
| Field | General mathematics |
| Keywords | 2-category 2-monad F-category Weak morphism Monadicity |
| Attached files | |
| 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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