Introduction The development of the formal theory of monads, begun in [23] and continued in [15], shows that much of the theory of monads [1] can be generalized from the setting of the 2-category Cat of small categories, functors and natural transformations to that of a general 2-category. The generalization, which involves defining the 2-category Mnd(K) of monads, monad maps and monad 2-cells ...

We introduce the notion of a distributive law between relative monad and monad. call this define it in any 2-category $\mathcal{K}$. In order to do that, we monads $\mathcal{K}$ with morphisms transformations as 1- 2-cells, respectively. relate our definition defined by Street. Thanks view prove two Beck-type theorems regarding laws. also describe what does mean have Eilenberg-Moore Kleisli obj...

Solutions of recursive program schemes over a given signature Σ were characterized by Bruno Courcelle as precisely the context-free (or algebraic) Σ-trees. These are the finite and infinite Σ-trees yielding, via labelling of paths, context-free languages. Our aim is to generalize this to finitary endofunctors H of general categories: we construct a monad CH “generated” by solutions of recursive...

Automatically identifying frequent composite patterns in DNA sequences is an important task in bioinformatics, especially when all the basic elements (or monad patterns) of a composite pattern are weak. In this paper, we compare one straightforward approach to assemble the monad patterns into composite patterns to two other rather complex approaches. Both our theoretical analysis and empirical ...

After a review of the concept of ‘‘monad with arities’’ we show that the category of algebras for such a monad has a canonical dense generator. This is used to extend the correspondence between finitary monads on sets and Lawvere’s algebraic theories to a general correspondence between monads and theories for a given category with arities. As an application we determine arities for the free gro...

Structural synthesis creates a structural scheme according to the given characteristics - degree of abnormality structure S and its irrationality s . is created at first stage synthesis, containing only rotational kinematic pairs corresponds abnormality, which ensured by ratio units – plus monads, minus monads null monads. At second stage, independence makes it possible bring obtained downgradi...

We present a general coalgebraic setting in which we define finite and infinite behaviour with B\"uchi acceptance condition for systems whose type is monad. The first part of the paper devoted to presenting construction monad suitable modelling (in)finite behaviour. second focuses on concepts (coalgebraic) automaton its ($\omega$-) end Kleene-type theorems regular input. framework instantiated ...

We describe the concurrency monad of the functional language Opal, which realizes a smooth integration of concurrent processes in a purely functional framework , providing a general choice and client-server based communication. We develop an axiomatic semantics for the concurrency monad using a variant of temporal interval logic as syntactic sugar on top of the logic of computable functions .