Monads with arities and their associated theories
نویسندگان
چکیده
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 an application we determine arities for the free groupoid monad on involutive graphs and recover the symmetric simplicial nerve characterisation of groupoids. © 2012 Elsevier B.V. All rights reserved.
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