some image logo

HOME

SEARCH

CURRENT ISSUE

REGULAR ISSUES

   Volume 1 (2005)

   Volume 2 (2006)

   Volume 3 (2007)

   Volume 4 (2008)

   Volume 5 (2009)

   Volume 6 (2010)

   Volume 7 (2011)

   Volume 8 (2012)

   Volume 9 (2013)

   Volume 10 (2014)

   Volume 11 (2015)

      Issue 1

      Issue 2

      Issue 3

      Issue 4

   Volume 12 (2016)

   Volume 13 (2017)

SPECIAL ISSUES

SURVEY ARTICLES

AUTHORS

ABOUT

SERVICE

LOGIN

FAQ

SUPPORT

CONTACT

VOLUME 11, ISSUE 1, PAPER 3


Monads need not be endofunctors

©Thorsten Altenkirch, University of Nottingham
©James Chapman, Institute of Cybernetics
©Tarmo Uustalu, Institute of Cybernetics

Abstract
We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed lambda-calculus syntax and indexed containers. We show that the Kleisli and Eilenberg-Moore constructions carry over to relative monads and are related to relative adjunctions. Under reasonable assumptions, relative monads are monoids in the functor category concerned and extend to monads, giving rise to a coreflection between relative monads and monads. Arrows are also an instance of relative monads.

Publication date: March 6, 2015

Full Text: PDF | PostScript
DOI: 10.2168/LMCS-11(1:3)2015

Hit Counts: 5426

Creative Commons