A category may bear many monoidal structures, but (to within a unique isomorphism) only one structure of “category with finite products”. To capture such distinctions, we consider on a 2-category those 2-monads for which algebra structure is essentially unique if it exists, giving a precise mathematical definition of “essentially unique” and investigating its consequences. We call such 2-monads...

A category may bear manymonoidal structures, but (to within a unique isomorphism) only one structure of \category with nite products". To capture such distinctions, we consider on a 2-category those 2-monads for which algebra structure is essentially unique if it exists, giving a precise mathematical de nition of \essentially unique" and investigating its consequences. We call such 2-monads pro...

The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly [15], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [1...

A category may bear many monoidal structures, but (to within a unique isomorphism) only one structure of \category with nite products". To capture such distinctions, we consider on a 2-category those 2-monads for which algebra structure is essentially unique if it exists, giving a precise mathematical deenition of \essentially unique" and investigating its consequences. We call such 2-monads pr...

Notions of guardedness serve to delineate admissible recursive definitions in various settings a compositional manner. In recent work, we have introduced an axiomatic notion symmetric monoidal categories, which serves as unifying framework for examples from program semantics, process algebra, and beyond. the present paper, propose generic metalanguage guarded iteration based on combining this w...

Recent investigations of lax algebras—in generalization of Barr’s relational algebras—make an essential use of lax extensions of monad functors on Set to the category Rel(V) of sets and V-relations (where V is a unital quantale). For a given monad there may be many such lax extensions, and different constructions appear in the literature. The aim of this article is to shed a unifying light on t...

Completely iterative monads of Elgot et al. are the monads such that every guarded iterative equation has a unique solution. Free completely iterative monads are known to exist on every iteratable endofunctor H, i. e., one with final coalgebras of all functors H( ) + X. We show that conversely, if H generates a free completely iterative monad, then it is iteratable.

We investigate monads of partiality in Martin-Löf type theory, following Moggi’s general monad-based method for modelling effectful computations. These monads are often called lifting monads and appear in category theory with different but related definitions. In this paper, we unveil the relationship between containers and lifting monads. We show that the lifting monads usually employed in typ...

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...