Related papers: Semi-Cosimplicial Objects and Spreadability
When modeling geostatistical or areal data, spatial structure is commonly accommodated via a covariance function for the former and a neighborhood structure for the latter. In both cases the resulting spatial structure is a consequence of…
Two high-level "pictures" of probability theory have emerged: one that takes as central the notion of random variable, and one that focuses on distributions and probability channels (Markov kernels). While the channel-based picture has been…
We study a category of probability spaces and measure-preserving Markov kernels up to almost sure equality. This category contains, among its isomorphisms, mod-zero isomorphisms of probability spaces. It also gives an isomorphism between…
We define a category $\mathsf{List}$ whose objects are sets and morphisms are mappings which assign to an element in the domain an ordered sequence (list) of elements in the codomain. We introduce and study a category of simplicial objects…
Let $k$ be a field, and let $\mathcal{C}$ be a Cauchy complete $k$-linear braided category with finite dimensional morphism spaces and ${{\rm End}(\bf 1)}=k$. We call an indecomposable object $X$ of $\mathcal C$ non-negligible if there…
In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial…
In this follow-up to [16], we continue developing the notion of a lego category and its many applications to stratifiable spaces and the computation of their Grothendieck classes. We illustrate the effectiveness of this construction by…
In this paper, we introduce the category of brace triples in a braided monoidal setting and prove that it is isomorphic to the category of s-Hopf braces, which are a generalization of cocommutative Hopf braces. After that, we obtain a…
Given a category, one may construct slices of it. That is, one builds a new category whose objects are the morphisms from the category with a fixed codomain and morphisms certain commutative triangles. If the category is a groupoid, so that…
We build a model structure from the simple point of departure of a structured interval in a monoidal category - more generally, a structured cylinder and a structured co-cylinder in a category.
In this paper analogically as quadratic stochastic operators and processes we define cubic stochastic operator (CSO) and cubic stochastic processes (CSP). These are defined on the set of all probability measures of a measurable space. The…
We show that every braiding on a monoidal bicategory induces a monoidal structure on its bicategory of monoids, such that if the former is sylleptic or symmetric then the latter is braided or symmetric, respectively. This extends a classic…
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…
Harnessing the predictive capability of Markov process models requires propagating probability density functions (beliefs) through the model. For many existing models however, belief propagation is analytically infeasible, requiring…
I provide analytical or semi-analytical expressions for the small-angle scattering of colloidal objects that can be described as curved plates. These models could help characterize a variety of inorganic or biological systems.
Semi-entwining structures are proposed as concepts simpler than entwining structures, yet they are shown to have interesting applications in constructing intertwining operators and braided algebras, lifting functors, finding solutions for…
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…
We construct explicitly the weights on the simplicial category so that the colimits and limits of 2-functors with those weights provide the Kleisli objects and the Eilenberg-Moore objects, respectively, in any 2-category.
A general method for lifting weak factorization systems in a category S to model category structures on simplicial objects in S is described, analogously to the lifting of cotorsion pairs in Abelian categories to model category structures…
Equivariant monoids are very important objects in many branches of mathematics: they combine the notion of multiplication and the concept of a group action. In this paper we will construct categories which encode the structure borne by…