Monads provide a way of structuring functional programs. Most real applications require a combination of primitive monads. Here we describe how some monads may be combined with others to yield a combined monad.

Monads are extensively used nowadays to abstractly model a wide range of computational effects such as nondeterminism, statefulness, and exceptions. It turns out that equipping a monad with a (uniform) iteration operator satisfying a set of natural axioms allows for modelling iterative computations just as abstractly. The emerging monads are called complete Elgot monads. It has been shown recen...

This paper is a contribution to the search for efficient and high-level mathematical tools specify reason about (abstract) programming languages or calculi. Generalising reduction monads of Ahrens et al., we introduce transition monads, thus covering new applications such as lambda-bar-mu-calculus, pi-calculus, Positive GSOS specifications, differential lambda-calculus, big-step, simply-typed, ...

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.

Graded monoidal categories were introduced by Frohlich and C.T.C. ̈ Wall in 8 , where they presented a suitable abstract setting to study the Brauer group in equivariant situations. This paper is concerned with the analysis and classification of these graded monoidal categories, following a parallel treatment to that made in 2 for the non-monoidal case. In any graded monoidal category, its 1-com...