Compound Monads and the Kleisli Category
نویسنده
چکیده
We consider sets of monad rules derived by focussing on the Kleisli category of a monad, and from these we derive some constructions for compound monads. Under certain conditions these constructions correspond to a distributive law connecting the monads. We also show how these relate to some constructions for compound monads described previously.
منابع مشابه
Applications of the Kleisli and Eilenberg-Moore 2-adjunctions
In 2010, J. Climent Vidal and J. Soliveres Tur developed, among other things, a pair of 2-adjunctions between the 2-category of adjunctions and the 2-category of monads. One is related to the Kleisli adjunction and the other to the Eilenberg-Moore adjunction for a given monad.Since any 2-adjunction induces certain natural isomorphisms of categories, these can be used to classify bijection...
متن کاملA cottage industry of lax extensions
In this work, we describe an adjunction between the comma category of Set-based monads under the V -powerset monad and the category of associative lax extensions of Set-based monads to the category of V -relations. In the process, we give a general construction of the Kleisli extension of a monad to the category of V-relations.
متن کاملKleisli and Eilenberg-Moore Constructions as Parts of Biadjoint Situations
We consider monads over varying categories, and by defining the morphisms of Kleisli and of Eilenberg-Moore from a monad to another and the appropriate transformations (2-cells) between morphisms of Kleisli and between morphisms of Eilenberg-Moore, we obtain two 2-categories MndKl and MndEM. Then we prove that MndKl and MndEM are, respectively, 2-isomorphic to the conjugate of Kl and to the tra...
متن کاملFreyd is Kleisli, for Arrows
Arrows have been introduced in functional programming as generalisations of monads. They also generalise comonads. Fundamental structures associated with (co)monads are Kleisli categories and categories of (Eilenberg-Moore) algebras. Hence it makes sense to ask if there are analogous structures for Arrows. In this short note we shall take first steps in this direction, and identify for instance...
متن کاملOrder-adjoint monads and injective objects
Given a monad T on Set whose functor factors through the category of ordered sets with left adjoint maps, the category of Kleisli monoids is defined as the category of monoids in the hom-sets of the Kleisli category of T. The Eilenberg-Moore category of T is shown to be strictly monadic over the category of Kleisli monoids. If the Kleisli category of T moreover forms an order-enriched category,...
متن کامل