Related papers: Classical Distributive Restriction Categories
We give an alternative proof of the general chain rule for functions of bounded variation ([ADM90]), which allows to compute the distributional differential of $\varphi\circ F$, where $\varphi\in \mathrm{LIP}(\mathbb{R}^m)$ and…
It is common to encounter symmetric monoidal categories $\mathcal{C}$ for which every object is equipped with an algebraic structure, in a way that is compatible with the monoidal product and unit in $\mathcal{C}$. We define this formally…
We show that the noncommutative residue density, resp. the cut-off regularised integral are the only closed linear, resp. continuous closed linear forms on certain classes of symbols. This leads to alternative proofs of the uniqueness of…
The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we study this problem in the context of categorical probability…
In probabilistic modelling, joint distributions are often of more interest than their marginals, but the standard composition of stochastic channels is defined by marginalization. Last year at ACT, the notion of 'copy-composition' was…
A braided Ann-category $\A$ is an Ann-category $\A$ together with the braiding $c$ such that $(\A, \otimes, a, c, (I,l,r))$ is a braided tensor category, and $c$ is compatible with the distributivity constraints. The paper shows the…
In categorical realizability, it is common to construct categories of assemblies and categories of modest sets from applicative structures. These categories have structures corresponding to the structures of applicative structures. In the…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction…
The statistical mechanical partition function can be used to construct different forms of phase space distributions not restricted to the Gibbs-Boltzmann factor. With a generalised Lorentzian both the Kappa-Bose and Kappa-Fermi partition…
Categorical predictors are omnipresent in everyday regression practice: in fact, most regression data involve some categorical predictors, and this tendency is increasing in modern applications with more complex structures and larger data…
This work mainly concerns the -- here introduced -- category of $\mathscr Q$-sets and functional morphisms, where $\mathscr Q$ is a commutative semicartesian quantale. We describe, in detail, the limits and colimits of this complete and…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
In this paper we analyze the classical limit of the Nelson model with cut off, when both non-relativistic and relativistic particles number goes to infinity. We prove convergence of quantum observables to the solutions of classical…
First of all, we recall the well known notion of semidirect product both for classical algebraic structures (like groups and rings) and for more recent ones (digroups, left skew braces, heaps, trusses). Then we analyse the concept of…
As a practical foundation for a homotopy theory of abstract spacetime, we extend a category of certain compact partially ordered spaces to a convenient category of locally preordered spaces. In particular, we show that our new category is…
This paper is the continuation of the research of the author and his colleagues of the {\it canonical} decomposition of graphs. The idea of the canonical decomposition is to define the binary operation on the set of graphs and to represent…
Consider a commutative monoid $(M,+,0)$ and a biadditive binary operation $\mu \colon M \times M \to M$. We will show that under some additional general assumptions, the operation $\mu$ is automatically both associative and commutative. The…
Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is…
Many important statistical models fall outside classical moment-based methods due to the non-existence of moments or moment generating functions. We propose a generalised probabilistic framework in which densities are replaced by pairs…