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hal-00702041, version 1

Monads with arities and their associated theories

Clemens Berger, paul-andré melliès 1, Mark Weber 2

Journal of Pure and Applied Algebra 216, 8-9 (2012) 2029-2048

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.

  • 1:  Preuves, Programmes et Systèmes (PPS)
  • CNRS : UMR7126 – Université Paris VII - Paris Diderot
  • 2:  Macquarie University
  • University of Sydney
  • Domain : Mathematics/Category Theory
  • Comment : 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
 
  • hal-00702041, version 1
  • http://hal.archives-ouvertes.fr/hal-00702041
  • oai:hal.archives-ouvertes.fr:hal-00702041
  • From: Paul-André Melliès <>
  • Submitted on: Tuesday, 29 May 2012 10:09:19
  • Updated on: Tuesday, 29 May 2012 10:09:19