Pseudo-distributive Laws
نویسندگان
چکیده
منابع مشابه
Pseudo-distributive laws
We address the question of how elegantly to combine a number of different structures, such as finite product structure, monoidal structure, and colimiting structure, on a category. Extending work of Marmolejo and Lack, we develop the definition of a pseudo-distributive law between pseudo-monads, and we show how the definition and the main theorems about it may be used to model several such stru...
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In this paper, we give a novel abstract description of Szabo’s polycategories. We use the theory of double clubs – a generalisation of Kelly’s theory of clubs to ‘pseudo’ (or ‘weak’) double categories – to construct a pseudo-distributive law of the free symmetric strict monoidal category pseudocomonad onMod over itself qua pseudomonad, and show that monads in the ‘two-sided Kleisli bicategory’ ...
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The formal theory of monads, originally introduced by Street in [22] and developed further by Lack and Street [17] provides a mathematically efficient treatment of several aspects of the theory of monads [1]. For example, it exhibits a universal property of the category of algebras for a monad and provides a clear explanation for Beck’s axioms for a distributive law [2]. Over the past few years...
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Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond...
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We give a framework for combining n monads on the same category via distributive laws satisfying Yang-Baxter equations, extending the classical result of Barr and Wells which combines two monads via one distributive law. We show that this corresponds to iterating n-times the process of taking the 2-category of monads in a 2-category, extending the result of Street characterising distributive la...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2003
ISSN: 1571-0661
DOI: 10.1016/s1571-0661(03)50012-3