Related papers: Using Category Theory in Modeling Generics in OOP …
We study a certain type of action of categories on categories and on operads. Using the structure of the categories {\Delta} and {\Omega} governing category and operad structures, respectively, we define categories which instead encode the…
Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
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…
Categorical responses arise naturally within various scientific disciplines. In many circumstances, there is no predetermined order for the response categories, and the response has to be modeled as nominal. In this study, we regard the…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
Algebraic structures such as monoids, groups, and categories can be formulated within a category using commutative diagrams. In many common categories these reduce to familiar cases. In particular, group objects in Grp are abelian groups,…
The concept of functionality oriented programming is proposed, and some of its aspects are discussed, such as: (1) implementation independent basic types and generic collection types; (2) syntax requirements and recommendations for…
Automatic or assisted workflow composition is a field of intense research for applications to the world wide web or to business process modeling. Workflow composition is traditionally addressed in various ways, generally via theorem proving…
The representation of workflows and processes is essential in materials science engineering, where experimental and computational reproducibility depend on structured and semantically coherent process models. Although numerous ontologies…
Building models of the world from observation, i.e., induction, is one of the major challenges in machine learning. In order to be useful, models need to maintain accuracy when used in novel situations, i.e., generalize. In addition, they…
Object Oriented Design methodology is an emerging software development approach for complex systems with huge set of requirements. Unlike procedural approach, it captures the requirements as a set of data rather than services, encapsulated…
The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a…
In this paper, we describe a general theory of modules over an algebra over an operad. We also study functors between categories of modules. Specializing to the operad E_d of little d-dimensional disks, we show that each (d-1)-manifold…
Object-oriented programming languages such as Java and Objective C have become popular for implementing agent-based and other object-based simulations since objects in those languages can {\em reflect} (i.e. make runtime queries of an…
Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…
We adapt the technique of type-generic programming via descriptions pointing into a universe to the domain of typed languages with binders and variables, implementing a notion of "syntax-generic programming" in a dependently typed…
We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega,…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…