Related papers: Extending Resource Monotones using Kan Extensions
We introduce and discuss the notion of monotonicity for the complexity measures of general probability distributions, patterned after the resource theory of quantum entanglement. Then, we explore whether this property is satisfied by the…
Resource theory is a widely-applicable framework for analyzing the physical resources required for given tasks, such as computation, communication, and energy extraction. In this paper, we propose a general scheme for analyzing resource…
A wide class of coupled-cluster methods is introduced, based on Arponen's extended coupled-cluster theory. This class of methods is formulated in terms of a coordinate transformation of the cluster operators. The mathematical framework for…
The resource theory of quantum superposition is an extension of the quantum coherent theory, in which linear independence relaxes the requirement of orthogonality. It can be used to quantify the nonclassical in superposition of finite…
We specialise a recently introduced notion of generalised dinaturality for functors $T : (\mathcal{C}^\text{op})^p \times \mathcal{C}^q \to \mathcal{D}$ to the case where the domain (resp., codomain) is constant, obtaining notions of ends…
Search trees are fundamental data structures in computer science. We study functionals on random search trees that satisfy recurrence relations of a simple additive form. Many important functionals including the space requirement, internal…
Mayer cluster expansion is an important tool in statistical physics to evaluate grand canonical partition functions. It has recently been applied to the Nekrasov instanton partition function of $\mathcal{N}=2$ 4d gauge theories. The…
In this article we develop formal category theory within augmented virtual double categories. Notably we formalise the classical notions of Kan extension, Yoneda embedding $\text y_A\colon A \to \hat A$, exact square, total category and…
We present {Kanren} (read: set-Kanren), an extension to miniKanren with constraints for reasoning about sets and association lists. {Kanren} includes first-class set objects, a functionally complete family of set-theoretic constraints…
The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an…
We study Kan extensions in three weakenings of the Eilenberg-Moore double category associated to a double monad, that was introduced by Grandis and Par\'e. To be precise, given a normal oplax double monad $T$ on a double category $\mathcal…
We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.
A fundamental challenge in quantum resource theory is to establish operational interpretations by quantifying the advantage that quantum resources provide in specific tasks. Conventional resource theories, however, have inherent limitations…
The perturbation expansion of the solution of a fixed point equation or of an ordinary differential equation may be expressed as a power series in the perturbation parameter. The terms in this series are indexed by rooted trees and depend…
Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.
ProbNetKAT is a probabilistic extension of NetKAT with a denotational semantics based on Markov kernels. The language is expressive enough to generate continuous distributions, which raises the question of how to compute effectively in the…
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…
Quantum resource theories offer a powerful framework for studying various phenomena in quantum physics. Despite considerable effort has been devoted to developing a unified framework of resource theories, there are few common properties…
In this dissertation we examine enrichment relations between categories of dual structure and we sketch an abstract framework where the theory of fibrations and enriched category theory are appropriately united. We initially work in the…
We study how to infer new choices from prior choices using the framework of choice functions, a unifying mathematical framework for decision-making based on sets of preference orders. In particular, we define the natural (most conservative)…