Monads with arities and their associated theories
Category Theory
2016-04-04 v2
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.
Cite
@article{arxiv.1101.3064,
title = {Monads with arities and their associated theories},
author = {Clemens Berger and Paul-André Melliès and Mark Weber},
journal= {arXiv preprint arXiv:1101.3064},
year = {2016}
}
Comments
New introduction; Section 1 shortened and redispatched with Section 2; Subsections on symmetric operads (3.14) and symmetric simplicial sets (4.17) added; Bibliography completed