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    ohad (ohad@mathstodon.xyz)'s status on Saturday, 30-Nov-2024 06:11:06 JSTohadohad
    in reply to
    • julesh

    @julesh I'd start here: https://arxiv.org/abs/1101.3064

    In conversationabout 6 months ago from mathstodon.xyzpermalink

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    1. Domain not in remote thumbnail source whitelist: arxiv.org
      Monads with arities and their associated theories
      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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