Related papers: Order Unit Spaces and Probabilistic Models
Ordered locally convex spaces is an important classes of spaces in the theory of ordered topological vector spaces just as locally convex spaces in the theory of topological vector spaces. Some special classes of ordered locally convex…
We classify which dual functors on a unitary multitensor category are compatible with the dagger structure in terms of groupoid homomorphisms from the universal grading groupoid to $\mathbb{R}_{>0}$ where the latter is considered as a…
Given an operad $\mathcal{O}$, we define a notion of weak $\mathcal{O}$-monoids -- which we term $\mathcal{O}$-pseudomonoids -- in a 2-category. In the special case with the 2-category in question is the 2-category $\mathsf{Cat}$ of…
We prove that any right Quillen functor between arbitrary model categories admits non trivial functorial factorizations that are similar to those of a model structure. We also prove that these factorizations can be made for lax monoidal…
For the functors acting in the category of compact Hausdorff spaces, we introduce the so-called open multi-commutativity property, which generalizes both bicommutativity and openness, and prove that this property is satisfied by the functor…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…
We extend the theory of Sweeder's measuring comonoids to the framework of duoidal categories: categories equipped with two compatible monoidal structures. We use one of the tensor products to endow the category of monoids for the other with…
We explore an alternative definition of unit in a monoidal category originally due to Saavedra: a Saavedra unit is a cancellative idempotent (in a 1-categorical sense). This notion is more economical than the usual notion in terms of…
We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective…
This paper concerns a stochastic construction of probabilistic coherent spaces by employing novel ingredients (i) linear exponential comonads arising properly in the measure-theory (ii) continuous orthogonality between measures and…
In the theory of operads we consider functors of generalized symmetric powers defined by sums of coinvariant modules under actions of symmetric groups. One observes classically that the construction of symmetric functors provides an…
A PROP is a symmetric monoidal category whose objects are the nonnegative integers and whose tensor product on objects is addition. A morphism from $m$ to $n$ in a PROP can be visualized as a string diagram with $m$ input wires and $n$…
We explore the sense in which the existing constructions for higher-order maps on quantum theory based on causality constraints and compositionality constraints respectively, coincide. More precisely, we construct a functor F : Caus(C) ->…
The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful;…
A PROP is a symmetric monoidal category, whose set of objects is the set of natural numbers and on objects the monoidal structure is given by the addition. An algebra over a PROP is a symmetric strict monoidal functor to the tensor category…
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…
We provide conditions on a monoidal model category $\mathcal{M}$ so that the category of commutative monoids in $\mathcal{M}$ inherits a model structure from $\mathcal{M}$ in which a map is a weak equivalence or fibration if and only if it…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
We introduce the notion of order projections using the order unit property of a positive element in an order unit space and characterize them in terms of (geometric) orthogonality. We describe order projections of the order unit space…
The uniform probability measure on a convex polytope induces piecewise polynomial densities on its projections. For a fixed combinatorial type of simplicial polytopes, the moments of these measures are rational functions in the vertex…