In this paper we construct extensions of Set-monads – and, more generally, of lax Rel-monads – into lax monads of the bicategory Mat(V) of generalized V-matrices, whenever V is a well-behaved lattice equipped with a tensor product. We add some guiding examples.

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...

We prove that there is a full and faithful nerve functor defined on the category 2-Cat lax of 2-categories and (normal) lax 2-functors. This functor extends the usual notion of nerve of a category and it coincides on objects with the so-called geometric nerve of a 2-category or of a 2-groupoid. We also show that (normal) lax 2-natural transformations produce homotopies of a special kind, and th...

Korean has two types of voiceless alveolar fricatives One is called aspirated and the other tense (Kagaya, 1974) The aspirated fricatives have also been called lax fricatives because phonolog1cally they act hke a lax obstruent, undergomg a set of processes that lax stops do For example, Korean lax stops and Isl undergo post-obstruent tensmg {Sohn 1999) Aspirated stops (e g, ch), however, do not...

Despite playing a central role in tolerance, little is known regarding the mechanism by which intracellular CTLA-4 is shuttled from the trans-Golgi network to the surfaces of T cells. In this context, Ras-related GTPase Rab8 plays an important role in the intracellular transport, while we have previously shown that CTLA-4 binds to the immune cell adaptor TRIM in T cells. In this study, we demon...

We show that the m-dimensional Euler–Manakov top on so∗(m) can be represented as a Poisson reduction of an integrable Hamiltonian system on a symplectic extended Stiefel variety V̄(k,m), and present its Lax representation with a rational parameter. We also describe an integrable two-valued symplectic map B on the 4dimensional variety V(2, 3). The map admits two different reductions, namely, to t...

A Bargmann symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the Dirac systems. It is shown that the spatial part of the nonlinearized Lax pairs and adjoint Lax pairs is a finite dimensional Liouville integrable Hamiltonian system and that under the control of the spatial part, the time parts of the nonlinearized Lax pairs and adjoint Lax pairs are interpreted as a ...