Related papers: Idempotence for relative monads
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
We establish a duality between monads and monadic morphisms in any $(\infty,2)$-category and characterize monadic morphisms in a wide class of examples. This duality unifies several dualities between algebraic structures and their…
Given an operad A of topological spaces, we consider A-monads in a topological category C . When A is an A-infinity-operad, any A-monad K : C -> C can be thought of as a monad up to coherent homotopies. We define the completion functor with…
In contrast to classical strongly continuous semigroups, the study of bi-continuous semigroups comes with some freedom in the properties of the associated locally convex topology. This paper aims to give minimal assumptions in order to…
We define a relative property A for a countable group with respect to a finite family of subgroups. Many characterizations for relative property A are given. In particular a relative bounded cohomological characterization shows that if a…
The paper develops further the theory of quandle rings which was introduced by the authors in a recent work. Orderability of quandles is defined and many interesting examples of orderable quandles are given. It is proved that quandle rings…
We obtain analytical expressions for an effective potential of interaction between two- and three-dimensional (2D and 3D) solitons (including the case of 2D vortex solitons) belonging to two different modes which are incoherently coupled by…
We showed that isomorphism classes of idempotent evolution algebras are in bijection with the orbits of the semidirect product group of the symmetric group and the torus, considered the combinatoric problem of enumeration of isomorphism…
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
We determine when contractive idempotents in the measure algebra of a locally compact group commute. We consider a dynamical version of the same result. We also look at some properties of groups of measures whose identity is a contactive…
We characterise the elements of the (maximum) idempotent generated subsemigroup of the Kauffman monoid in terms of combinatorial data associated to certain normal forms. We also calculate the smallest size of a generating set and idempotent…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
We introduce the notion of a distributive law between a relative monad and a monad. We call this a relative distributive law and define it in any 2-category $\mathcal{K}$. In order to do that, we introduce the 2-category of relative monads…
Given a monoidal $\infty$-category $C$ equipped with a monoidal recollement, we give a simple criterion for an object in $C$ to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them.…
We study the homology of pointed sets over a partially commutative monoid.
T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions. The resulting T-dual theories contain novel nonlocal fields. These fields represent dipoles of constant magnitude.…
In this note, it is shown that the nilpotency of submatrices of a certain class of adjacency matrices is equivalent to the aperiodic Collatz conjecture.
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relating them, e.g. knot theory or the theory of manifolds with…
The category $_{A}\mathbb{S}_{A}$ of bisemimodules over a semialgebra $A,$ with the so called Takahashi's tensor product $-\boxtimes_{A}-,$ is semimonoidal but not monoidal. Although not a unit in $_{A}\mathbb{S}%_{A},$ the base semialgebra…