Monads with arities and their associated theories

Details Monads with arities and their associated theories Monads with arities and their associated theories

2011-01-16

arxiv.org/abs/1101.3064v2

Mathematics

Category Theory

New introduction; Section 1 shortened and redispatched with Section 2; Subsections on symmetric operads (3.14) and symmetric s

Scientific paper

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.

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