Monads with arities and their associated theories
Abstract
After a review of the concept of "monad with arities" we show that the category of algebras for such a monad has a canonical dense generator. This is used to extend the correspondence between finitary monads on sets and Lawvere's algebraic theories to a general correspondence between monads and theories for a given category with arities. As application we determine arities for the free groupoid monad on involutive graphs and recover the symmetric simplicial nerve characterisation of groupoids.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2011
- DOI:
- 10.48550/arXiv.1101.3064
- arXiv:
- arXiv:1101.3064
- Bibcode:
- 2011arXiv1101.3064B
- Keywords:
-
- Mathematics - Category Theory;
- Primary 18C10;
- 18C15;
- Secondary 18D50;
- 18B40
- E-Print:
- New introduction