Related papers: Noncommutative orders. A preliminary study
Fusion categories are fundamental objects in quantum algebra, but their definition is narrow in some respects. By definition a fusion category must be k-linear for some field k, and every simple object V is strongly simple, meaning that (V)…
We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…
Preordered semialgebras and semirings are two kinds of algebraic structures occurring in real algebraic geometry frequently and usually play important roles therein. They have many interesting and promising applications in the fields of…
Let $R$ be a not necessarily commutative ring with $1.$ In the present paper we first introduce a notion of quasi-orderings, which axiomatically subsumes all the orderings and valuations on $R$. We proceed by uniformly defining a coarsening…
We study coalgebraic modal logic to characterise behavioural equivalence in the presence of side effects, i.e., when coalgebras live in a (co)Kleisli or an Eilenberg-Moore category. Our aim is to develop a general framework based on indexed…
Given a countable transitive model of set theory and a partial order contained in it, there is a natural countable Borel equivalence relation on generic filters over the model; two are equivalent if they yield the same generic extension. We…
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…
In this exposition, we get examples of what is called a "linear hyperdoctrine", based on categories of comodules indexed by coalgebras. This structures can model first order linear logic.
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
A measurable relation algebra is a relation algebra in which the identity element is a sum of atoms that can be measured in the sense that the "size" of each such atom can be defined in an intuitive and reasonable way (within the framework…
Coherence phenomena appear in two different situations. In the context of category theory the term `coherence constraints' refers to a set of diagrams whose commutativity implies the commutativity of a larger class of diagrams. In the…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
Let $X$ be a topological space. A subset of $C(X)$, the space of continuous real-valued functions on $X$, is a partially ordered set in the pointwise order. Suppose that $X$ and $Y$ are topological spaces, and $A(X)$ and $A(Y)$ are subsets…
In this paper we propose a definition of a recurrence relation homomorphism and illustrate our definition with a few examples. We then define the period of a k-th order of linear recurrence relation and deduce certain preliminary results…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum invariants. We also review categorification, which adds an additional layer of…
We study a categorical condition on relations, which is a categorical formulation of J\'onsson's characterisation of congruence distributive varieties. Categories satisfying these conditions need not be varieties; for instance, the dual of…
Learning representations for semantic relations is important for various tasks such as analogy detection, relational search, and relation classification. Although there have been several proposals for learning representations for individual…
A classification, according to invariant theory, of non-constant invariant Abel ODEs known as solvable and found in the literature is presented. A set of new integrable classes depending on one or no parameters, derived from the analysis of…