Related papers: Bounded distributive lattices with strict implicat…
We introduce the notion of weak Lie 2-bialgebra. Roughly, a weak Lie 2-bialgebra is a pair of compatible 2-term $L_\infty$-algebra structures on a vector space and its dual. The compatibility condition is described in terms of the big…
We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial…
In this paper, we will study Heyting algebras endowed with tense negative operators, which we call tense H-algebras and we proof that these algebras are the algebraic semantics of the Intuitionistic Propositional Logic with Galois…
In this note we generalize the construction, due to Ghilardi, of the free Heyting algebra generated by a finite distributive lattice, to the case of arbitrary distributive lattices. Categorically, this provides an explicit construction of a…
We develop a duality for (modal) lattices that need not be distributive, and use it to study positive (modal) logic beyond distributivity, which we call weak positive (modal) logic. This duality builds on the Hofmann, Mislove and Stralka…
We investigate a class of combinatory algebras, called ribbon combinatory algebras, in which we can interpret both the braided untyped linear lambda calculus and framed oriented tangles. Any reflexive object in a ribbon category gives rise…
In braided tensor categories we show the Maschke's theorem and give the necessary and sufficient conditions for double cross biproducts and crossbiproducts and biproducts to be bialgebras. We obtain the factorization theorem for braided…
An artinian graded algebra, $A$, is said to have the Weak Lefschetz property (WLP) if multiplication by a general linear form has maximal rank in every degree. A vast quantity of work has been done studying and applying this property,…
In representation theory, the double centraliser property is an important property for a module (bimodule). It plays a fundamental role in many theories. In this paper, we extend this property to complexes in derived categories of finite…
Weak (Hopf) bialgebras are described as (Hopf) bimonoids in appropriate duoidal (also known as 2-monoidal) categories. This interpretation is used to define a category wba of weak bialgebras over a given field. As an application, the "free…
This paper fills a gap in the literature on natural duality theory. It concerns dual representations of categories of distributive-lattice-based algebras in which the lattice reducts are not assumed to have bounds. The development of theory…
We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the…
In this paper we introduce the notion of $\Delta$-weak character amenable Banach algebras and investigate $\Delta$-weak character amenability of certain Banach algebras such as projective tensor product $A\widehat{\otimes}B$, Lau product…
In this work, we have introduced and studied some basic geometric properties of extended weakly symmetric spaces. After classification of this structure we have also established the existence of such a space by presenting a non-trivial…
In this paper we present the Sweedler cohomology for a cocommutative weak Hopf algebra H. We show that the second cohomology group classifies completely the weak crossed products, having a common preunit, of H with a commutative left…
We study a class of formulas generalizing the weak law of the excluded middle, and provide a characterization of these formulas in terms of Kripke frames and Brouwer algebras. We use these formulas to separate logics corresponding to…
There are several prominent duality results in pointfree topology. The Hofmann-Lawson duality establishes that the category of continuous frames is dually equivalent to the category of locally compact sober spaces. This restricts to a dual…
In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSHalgebras bearing in mind the…
Let $(A,\Delta)$ be a weak multiplier Hopf algebra. It is a pair of a non-degenerate algebra $A$, with or without identity, and a coproduct $\Delta$ on $A$, satisfying certain properties. The main difference with multiplier Hopf algebras is…
We develop the bialgebra theory for two classes of non-associative algebras: nearly associative algebras and $LR$-algebras. In particular, building on recent studies that reveal connections between these algebraic structures, we establish…