Related papers: First Steps towards Categorical Algebraic Artifici…
In recent years, the modeling interest has increased significantly from the molecular level to the atomic and quantum scale. The field of computational chemistry plays a significant role in designing computational models for the operation…
A generalized algebra of quantum observables, depending on extra dimensional constants, is considered. Some limiting forms of the algebra are investigated and their possible applications to the descriptions of interactions of fundamental…
We introduce a mathematical framework for retrosynthetic analysis, an important research method in synthetic chemistry. Our approach represents molecules and their interaction using string diagrams in layered props - a recently introduced…
This paper is a first step to chase the ambitious objective of developing a mathmatical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors…
We give an introduction to constructive category theory by answering two guiding computational questions. The first question is: how do we compute the set of all natural transformations between two finitely presented functors like…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic scale structure of matter and its properties, involves transforming the Cartesian…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
A subclass of dynamical semigroups induced by the interaction of a quantum system with an environment is introduced. Such semigroups lead to the selection of a stable subalgebra of effective observables. The structure of this subalgebra is…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
We construct an abelian category C and exact functors in C which on the Grothendieck group descend to the action of a simply-laced quantum group in its adjoint representation. The braid group action in the adjoint representation lifts to an…
These are the notes for a minicourse held in Odessa (2016) and Belo Horizonte (2017). My aim was to provide a short introduction to basic notions of category theory and representation theory of finite-dimensional algebras. We learnt the…
Recent interest in human-AI interactions in agent-based modeling and simulation (ABMS) has grown rapidly due to the widespread utilization of large language models (LLMs). ABMS is an intelligent approach that simulates autonomous agents'…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…
We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
This article serves as a preliminary introduction to the design of a new, open-source applied and computational category theory framework, named Categorica, built on top of the Wolfram Language. Categorica allows one to configure and…
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…
Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas- and in the condensed phase. Together with recently developed and currently pursued efforts in…