Abstract
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 language | English |
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Pages (from-to) | 708-747 |
Number of pages | 40 |
Journal | Advances in Mathematics |
Volume | 252 |
DOIs | |
Publication status | Published - 15 Feb 2014 |
Externally published | Yes |
Keywords
- 2-category
- 2-monad
- F-category
- Monadicity
- Primary
- Weak morphism