Related papers: Presenting with Quantitative Inequational Theories
Formally verifying the properties of formal systems using a proof assistant requires justifying numerous minor lemmas about capture-avoiding substitution. Despite work on category-theoretic accounts of syntax and variable binding, raw,…
Ordering theorems, characterizing when partial orders of a group extend to total orders, are used to generate hypersequent calculi for varieties of lattice-ordered groups (l-groups). These calculi are then used to provide new proofs of…
We develop an extension of the process matrix (PM) framework for correlations between quantum operations with no causal order that allows multiple rounds of information exchange for each party compatibly with the assumption of well-defined…
Resent achievements in statistical theory, namely, a possibility to reproduce almost unlimited Mayer's activity series based on the information about their convergence radius, on the one hand, and generalization of the lattice statistics by…
We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality…
There are different notions of computation, the most popular being monads, applicative functors, and arrows. In this article we show that these three notions can be seen as monoids in a monoidal category. We demonstrate that at this level…
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally "centrality", i.e. the property for an effect to commute…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
Accounts of semantic phenomena often involve extending types of meanings and revising composition rules at the same time. The concept of monads allows many such accounts -- for intensionality, variable binding, quantification and focus --…
In this paper some reflections on the concept of transition are presented: groupoids are introduced as models for the construction of a ``generalized logic'' whose basic statements involve pairs of propositions which can be conditioned. In…
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging…
This in an introduction to the theory of non-commutative distributions of non-commuting operators or random matrices. Starting from the basic problem to find a good approach to the meaning of "non-commutative distribution" we will, in…
An algebraic theory, sometimes called an equational theory, is a theory defined by finitary operations and equations, such as the theories of groups and of rings. It is well known that algebraic theories are equivalent to finitary monads on…
This is the second paper in a series that aims to provide mathematical descriptions of objects and constructions related to the first few steps of the semantical theory of dependent type systems. We construct for any pair $(R,LM)$, where…
The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical…
This paper proposes a definition of recognizable transducers over monads and comonads, which bridges two important ongoing efforts in the current research on regularity. The first effort is the study of regular transductions, which extends…
Szlach\'anyi's skew monoidal categories are a well-motivated variation of monoidal categories in which the unitors and associator are not required to be natural isomorphisms, but merely natural transformations in a particular direction. We…
A new notion is introduced of matrix order indices which relate the matrix norm and its trace. These indices can be defined for any given matrix. They are especially important for matrices describing many-body systems, equilibrium as well…
In this survey paper we discuss some tools and methods which are of use in quasi-Monte Carlo (QMC) theory. We group them in chapters on Numerical Analysis, Harmonic Analysis, Algebra and Number Theory, and Probability Theory. We do not…
In this paper, we introduce and study two new classes of commutative rings, namely semi transitional rings and transitional rings, which extend several classical ideas arising from rings of continuous functions and their variants. A general…