Related papers: An equational approach to enriched distributivity

In this paper, we extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We achieve this by considering monoidal categories that are enriched in the category of Eilenberg-Moore algebras for a monad.…

The main concern of this paper is how to define proper measures of multipartite entanglement for mixed quantum states. Since the structure of partial separability and multipartite entanglement is getting complicated if the number of…

A model based on first-degree family relations network is used to describe the wealth distribution in societies. The network structure is not a-priori introduced in the model, it is generated in parallel with the wealth values through…

Motivated by Gentzen disjunction elimination rule in his Natural Deduction calculus and reading inequalities with meet in a natural way, we conceive a notion of distributivity for join-semilattices. We prove that it is equivalent to a…

We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which include weighted sums, linear…

We show that, under certain assumptions, strongly finitary enriched monads are given by discrete enriched Lawvere theories. On the other hand, monads given by discrete enriched Lawvere theories preserve surjections.

We prove an identity for five arguments, valid in the lattice of natural numbers with gcd and lcm as lattice operations. More generally, this identity characterizes arbitrary distributive lattices. Fixing three of the five arguments, we…

In this paper, we analyze the problem of how to adapt the concept of proportionality to situations where several perfectly divisible resources have to be allocated among certain set of agents that have exactly one claim which is used for…

By developing the Tanaka theory for rank 2 distributions, we completely classify classical Monge equations having maximal finite-dimensional symmetry algebras with fixed (albeit arbitrary) pair of its orders. Investigation of the…

We classify protocols of entanglement distribution as excessive and non-excessive ones. In a non-excessive protocol, the gain of entanglement is bounded by the amount of entanglement being communicated between the remote parties, while…

The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A…

We examine the distribution and popularity of different parameters (such as the number of descents, runs, valleys, peaks, right-to-left minima, and more) on the sets of increasing and flattened permutations. For each parameter, we provide…

Valuation based systems verifying an idempotent property are studied. A partial order is defined between the valuations giving them a lattice structure. Then, two different strategies are introduced to represent valuations: as infimum of…

A computational model for the distribution of wealth among the members of an ideal society is presented. It is determined that a realistic distribution of wealth depends upon two mechanisms: an asymmetric flux of wealth in trading…

We investigate the fair allocation of indivisible goods to agents with possibly different entitlements represented by weights. Previous work has shown that guarantees for additive valuations with existing envy-based notions cannot be…

Complementary correlations can reveal the genuine quantum correlations present in a composite quantum system. Here we investigate the relation between complementary correlations and other aspects of genuine quantum correlations. We show…

In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as…

We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…

Categorical universal algebra can be developed either using Lawvere theories (single-sorted finite product theories) or using monads, and the category of Lawvere theories is equivalent to the category of finitary monads on Set. We show how…

We develop a method to incrementally construct programming languages. Our approach is categorical: each layer of the language is described as a monad. Our method either (i) concretely builds a distributive law between two monads, i.e.…