2011/01/31 by Clemens Berger, Paul-André Melliès, Mark Weber · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Computer science #Homotopy and Cohomology in Algebraic Topology #Programming language #math.CT #msc:18B40 #msc:18C10 #msc:18C15 #msc:18D50
paper · pdf · doi:10.1016/j.jpaa.2012.02.039
published as J. Pure Appl. Algebra 216 (2012), 2029-2048 · 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
arxiv created 2011/02/10 · openalex publication_date 2012/04/10 · arxiv updated 2016/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.