10.2168/LMCS-11(1:3)2015
https://lmcs.episciences.org/928
Altenkirch, Thosten
Thosten
Altenkirch
Chapman, James
James
Chapman
Uustalu, Tarmo
Tarmo
Uustalu
Monads need not be endofunctors
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.
episciences.org
Computer Science - Programming Languages
Computer Science - Logic in Computer Science
Mathematics - Category Theory
2015-06-25
2015-03-06
2015-03-06
eng
journal article
arXiv:1412.7148
10.48550/arXiv.1412.7148
1860-5974
https://lmcs.episciences.org/928/pdf
VoR
application/pdf
Logical Methods in Computer Science
Volume 11, Issue 1
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