Monads need not be endofunctors
Monads need not be endofunctors
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DOI：
10.2168/lmcs-11(1:3)2015
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发表时间：
2010-03
期刊：
影响因子：
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通讯作者：
Thorsten Altenkirch;James Chapman;Tarmo Uustalu
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文献类型：
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作者：
Thorsten Altenkirch;James Chapman;Tarmo Uustalu
我们引入了一个广义的单子，称为相对单子，允许不同类别之间的底层函子。例子包括有限维向量空间、无类型和有类型的λ演算语法和索引容器。我们表明，Kleisli和Eilenberg-Moore结构结转到相对单子，并与相对排斥。在合理的假设下，相对单子是函子范畴中的幺半群，并扩展到单子，从而产生了单子和相对单子之间的共反射。箭头也是相对单子的一个实例。
We introduce a generalisation of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed λ-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 monads and relative monads. Arrows are also an instance of relative monads.