Related papers: Taming Multirelations
In this work, the partially and totally hom-coassociative ternary coalgebras are constructed and discussed. Their {infinitesimal} bialgebraic structures are also investigated. The related dual space structures and their properties are…
We study quadrangular properties of binary relations on a set $X$~--i.e., properties defined on configurations of four elements--~within an agonistic interpretation, where $xRy$ is interpreted as $x$ ``attacks''~$y$. Such relations induce a…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
We define the concept of a bi-operad. We develop the homotopy theory of "Bital-Sets" and of infinite-bi-operads. We develop a geometry of generalized schemes based on the spectra of distributive monochromatic bi-operads.
This chapter describes interrelations between: (1) algebraic structure on sets of scalars, (2) properties of monads associated with such sets of scalars, and (3) structure in categories (esp. Lawvere theories) associated with these monads.…
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
We review some concepts and properties of quantum correlations, in particular multipartite measures, geometric measures and monogamy relations. We also discuss the relation between classical and total correlations
A ringoid is a set with two binary operations that are linked by the distributive laws. We study special classes of ringoids that are congruence-simple or ideal-simple. In particular, we examine generalised parasemifields and…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
We generalise the Blok-J\'onsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and J\'onsson admit, in place…
In generalization of knot quandles we introduce similar algebraic structures associated with arbitrary pairs consisting of a path-connected topological space and its path-connected subspace.
We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…
We investigate how various forms of bisimulation can be characterised using the technology of logical relations. The approach taken is that each form of bisimulation corresponds to an algebraic structure derived from a transition system,…
A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…
Using a binary representation for basis elements of an algebra combined with a framework of multiplier and index functions, a connection has been established between the structure of a large class of algebras and the XOR componentwise…
This is a general introduction to duality in field theories. The existence and breaking of global symmetries is used as a guideline to systematically prove duality between different field theories. Systems discussed include abelian and…
We consider all 16 unary operations that, given a homogeneous binary relation R, define a new one by a boolean combination of xRy and yRx. Operations can be composed, and connected by pointwise-defined logical junctors. We consider the…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
General properties of ternary semigroups and groups are considered. The bi-element representation theory in which every representation matrix corresponds to a pair of elements is built, connection with the standard theory is considered and…
In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper, we have presented how partially ordered sets can be studied under simultaneous partially…