6
views
0
recommends
+1 Recommend
0 collections
    0
    shares
      • Record: found
      • Abstract: found
      • Article: found
      Is Open Access

      Distributive laws for relative monads

      Preprint

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We introduce the notion of a distributive law between a relative monad and a monad. We call this a relative distributive law and define it in any 2-category \(\mathcal{K}\). In order to do that, we introduce the 2-category of relative monads in a 2-category \(\mathcal{K}\) with relative monad morphisms and relative monad transformations as 1- and 2-cells, respectively. We relate our definition to the 2-category of monads in \(\mathcal{K}\) defined by Street. Thanks to this view we prove two Beck-type theorems regarding relative distributive laws. We also describe what does it mean to have Eilenberg-Moore and Kleisli objects in this context and give examples in the 2-category of locally small categories.

          Related collections

          Author and article information

          Journal
          25 July 2020
          Article
          2007.12982
          6e1766e9-90d7-4acd-993d-1be6efc1c8b6

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          18C15, 18C20, 18D05
          32 pages
          math.CT

          General mathematics
          General mathematics

          Comments

          Comment on this article