Category Theory Research Articles

The Implications of Cognitive Linguistics for English Vocabulary Teaching in Primary and Middle Schools from the Perspective of Basic Category Theory

Vocabulary teaching is an essential element of English teaching in middle schools and occupies a large proportion of the current English textbooks for primary and middle schools in China, but there are many problems with its vocabulary teaching. Basic category theory suggests that the process by which people develop an understanding of vocabulary formation and meaning is based on the perception of basic categories and their related relationships. This theory provides teachers with a new way of thinking about vocabulary teaching. Teaching vocabulary within the framework of basic category theory can help students grasp the scientific principles, philosophical views and cultural connotations embedded in English vocabulary, thus effectively improving their language ability and humanistic literacy.

Composing Cagean silence

In this article I model John Cage's pragmatics of silence using the mathematics of category theory with the framework of ontological logs. I use this approach in order to represent knowledge within Cage's so-called silent compositions – 4 ′ 33 ′′ , 0 ′ 00 ′′ (4 ′ 33 ′′ No. 2), and One 3 = 4 ′ 33 ′′ (0 ′ 00 ′′ ) + . I first generate a categorical schema F and an accompanying database that describes an instance of 4 ′ 33 ′′ from its premiere in 1952 which is translated via two functors into the categorical schema Z (0 ′ 00 ′′ ) and O (One 3 ). A pushout of Z and O along F allows for the presentation of the categorical schema S and its accompanying ontological log as an enfolding of Cage's pragmatics of silence. I then introduce the score Listening to John Cage listening in order to conceptualize the category of instances S - S e t , and further utilize it to investigate the language of S through its fibre order. I conclude by reporting on persistent spatio-temporal structures of Cagean silence embodied in S as meta-work.

Many-valued partial orders in a closed monoidal category

This paper introduces partially ordered Ω-monoidal relation systems on a category C endowed with a closed monoidal structure, and therewith explores a categorical theory of many-valued partial orders in C. For a fixed C-object Ω and a partially ordered Ω-monoidal relation system ϒ on C, the notion of a many-valued preordered (resp. many-valued partially ordered) C-object is formulated as a ϒ-preordered (resp. ϒ-partially ordered) C-object. Furthermore, the category of ϒ-preordered (resp. ϒ-partially ordered) C-objects is constructed and applied to quantale-valued preorders (resp. partial orders) on ordinary sets as well as on L-sets.

Model Theory Inspired by Grothendieckian Algebraic Geometry: a Survey of Sheaf Representations for Categorical Model Theory

Model Theory Inspired by Grothendieckian Algebraic Geometry: a Survey of Sheaf Representations for Categorical Model Theory

Green or Greenwashed? Examining Whether and When Consumers Are Able to Identify Greenwashing

In today's market, both companies and consumers face the challenge of navigating the pitfalls of greenwashing when it comes to a myriad of new and existing green products. This study examines consumer perceptions of such products and questions whether they can accurately identify greenwashing. Failure to do so could undermine a market for genuinely green products and have potentially detrimental effects on society and the environment. Drawing on categorization theory, consumers may categorize a new product as either honestly green, greenwashed, or regular based on prior knowledge of different green cues. We tested this ability using fictitious cleaning products in a within-subject experiment (N = 174) conducted in Germany and found that consumers often fall for greenwashing when asked solely about their purchase intentions. It seems that only when the participants are asked about the perceived greenness and greenwashing of the products are they able to spot the differences inherent to the green products. This research makes two academic contributions. First, our results extend the literature on consumer perceptions of green(washed) verbal and visual product cues. Second, we provide initial evidence against the implicit assumption in the greenwashing and green advertising literature that consumers can distinguish between greenwashed and honestly green products. Our findings provide potential guidance for practitioners in communicating sustainable product improvements without creating an impression of greenwashing. At the same time, this research may inform public policy regarding further measures needed to help consumers unmask greenwashing in purchase contexts.

Could ∞-Category Theory Be Taught to Undergraduates?

Could ∞-Category Theory Be Taught to Undergraduates?

Financial returns to corporate brand extensions: does typicality matter?

AbstractNews of extensions can cause stock price movements in the parent brand. Marketers extend brands into areas that vary in how typical they are of the parent brand. The degree of extension typicality can be an important cue for investors in their performance expectations of the brand. Integrating insights from Categorization Theory, Behavioral Finance, and Berlyne’s Two-Factor Theory, the authors argue that the impact of typicality on investor reactions depends upon the level of market exposure to a particular brand extension. Our study emphasizes that firms should take critical marketing actions to influence the buzz around the launch, depending on the extension’s typicality level. The results support our hypotheses. Particularly interesting is the finding that more atypical extensions become acceptable the greater market exposure to them (through marketing efforts as advertising and public relations).

Decomposing profile-to-role configurations in R&D-focused entrepreneurial teams

We draw on social categorization theory to explain how entrepreneurial teams focused on research and development (R&D) are configured to deliver successful new venture performance. Research on entrepreneurial teams tends to aggregate individuals to the team level, which helps distill the effects of complementarities among social categories of team members. Specifically, we examine how scientists and managers apply their unique profiles (i.e., accumulated skills and expertise) to execute their respective roles within entrepreneurial teams engaged in commercial scientific discovery. In line with the entrepreneurial team literature, we distinguish between “focused” and “diversified” social categorizations of principal scientists and managers. As such, we differentiate between individuals’ deep knowledge of a discipline and a background in two professional areas with relative expertise in each, likened to the “jack-of-all-trades”. We analyze how team profile-to-role configurations might result in different new venture outcomes being R&D performance and commercial performance. To examine our models, we use multi-source, longitudinal, secondary data drawn from 153 government-funded research-intensive ventures associated with the National Cancer Institute in the United States (U.S.). Our results reveal differential effects for R&D performance and commercial performance. We find that teams aiming to enhance their R&D performance should seek diversified principal scientists, whereas teams seeking commercial gains should appoint diversified managers. By the same token, diversified team members may bypass their own shortcomings and complement their strengths by attracting team members with focused social categorizations.

Comparison of Machine Learning Based on Category Theory

In recent years, machine learning has been widely used in data analysis of network engineering. The increasing types of model and data enhance the complexity of machine learning. In this paper, we propose a mathematical structure based on category theory as a combination of machine learning that combines multiple theories of data mining. We aim to study machine learning from the perspective of classification theory. Category theory utilizes mathematical language to connect the various structures of machine learning. We implement the representation of machine learning with category theory. In the experimental section, slice categories and functors are introduced in detail to model the data preprocessing. We use functors to preprocess the benchmark dataset and evaluate the accuracy of nine machine learning models. A key contribution is the representation of slice categories. This study provides a structural perspective of machine learning and a general method for the combination of category theory and machine learning.

Male nurse practice in inpatient rehabilitation. Finding a safe way: a grounded theory

BackgroundResearch interest in nursing's contribution to inpatient rehabilitation is growing. Nurses contribute to rehabilitation specifically by teaching patients how to care for themselves. This contribution is largely reported from a female or genderneutral perspective. Despite the work of male nurses being examined in a range of other specialities, their work within inpatient rehabilitation remains underexplored. ObjectiveTo report on a grounded theory study to identify and make visible male nurse practice in inpatient rehabilitation in Australia. DesignConstructivist grounded theory informed by symbolic interactionism. Setting(s)Stage 1 data were collected in locations of participants choosing throughout Australia. Stage 2 data collection centred on seven data collection sites across two specialist rehabilitation hospitals in two states of Australia. ParticipantsTwenty-three male nurses and 15 patients participated in the study. MethodsStage 1 (October 2013 to June 2014) consisted of semi-structured interviews with 11 male nurses. Stage 2 (February to April 2015) consisted of semi-structured interviews and 63.5 h of non-participant observation with 12 male nurses. Fifteen interviews with patients as recipients of male nurse care were also conducted. Data analysis included initial coding, focused coding, and theoretical coding using constant comparative methods, memo writing and diagramming. ResultsNurse participants were aware of patient perceptions about nursing being an occupation for women and male nurses being perceived as sexual threats, which led to an everyday concern of potential for misinterpretation. To address this concern, male nurses engaged in a three-phase process known as assessing and managing risk in order to minimise risk and to keep themselves safe in practice. However, two contextual conditions, type of care and urgency of care, influenced engagement in assessing and managing risk. The core category and substantive grounded theory to explain these results is finding a safe way. ConclusionsGender stereotypes affected the daily working lives of male nurses in inpatient rehabilitation. To counter the risk of misinterpretation male nurses used a range of strategies to address the barriers encountered daily in their working lives.However, male nurse efforts were often influenced by conditions outside of their control. In inpatient rehabilitation, male nurses practised cautiously to keep themselves safe in order to practise nursing.

Mathematics of Classifications, Chu spaces and the Continuum

We call classification the operation consisting of distributing objects in classes or groups which are, in general, less numerous than them. The relations between these classes may be (or not) partially or totally ordered. So there exist many kinds of classification schemes. Formally speaking, a classification may be a lattice, a semilattice, a chain, a hypergraph, a matroid, a tree, etc. Our purpose is to find the underlying mathematical structure of all these classifications. We explain how we can represent them in a unique way, constituting what has been called before a ”metaclassification” and which is, in fact, a Chu space. Thus, category theory can describe in terms of morphisms different operations on classifications that, according to Barwise and Seligman, we report in the following. Finally, we show that such a ”metaclassification” is the fundamental brick from which we can get some information about the mathematical continuum.

Cultural diversity in semi-virtual teams: A multicultural esports team study.

How does cultural diversity influence the performance of semi-virtual teams? We use the prism of esports and insights from virtual identity research and social categorization theory to determine the effect on semi-virtual teams in which member interaction is not necessarily mediated or constrained by physical world sociocultural norms. The common ground that has developed in esports results in a superordinate, culture-free gamer identity that transcends the virtual and physical worlds, and thus multicultural teams can enjoy the benefits of diverse knowledge without suffering unduly from social disintegration when gamer identity is salient-a reality challenged less in the virtual world than in the physical one. We conduct an empirical study using data from 4035 League of Legends games played by 102 multicultural teams from 2017 to 2020. Our results show that cultural diversity improves the quality of team strategy when gamer identity becomes more salient, and that that may come about when players are intensely exposed to the game world, when they play with many different virtual characters, and when they play at home court.

The Concept of Formation of Intelligent Control Systems of Power Supply of Urban Networks

Modern capabilities of intelligent control systems are increasingly being used in areas previously considered the exclusive work of people — experts with relevant experience in a particular field. Machine learning capabilities in the field of electric power industry, obtaining forecasts based on the data of intelligent sensors of various purposes are not an exception. At present the Russian Government has adopted a program for the development of the manufacturing industry until the end of 2035: during this time manufacturing output should grow by 192 %. It is obvious that this program should also meet the requirements of the modern scientific concept of industrial revolution "Industry 4.0", when manufacturing enterprises and corporations begin to develop and apply subsystems and elements of "smart manufacturing", which help to build intelligent communications between individual tasks and operations during the entire life cycle of production, in accordance with the principles and methods of systems engineering. It is important to note that the issues of intelligent management in the subject-oriented area of electric power industry (in our case — energy saving), as the basis of any industrial production in modern conditions, require the development and implementation, first of all, of new solutions based on modern IT-technologies. It is known that energy intensity in Russia, according to the World Bank, is 3-4 times lower than in European countries. It is also known that in connection with the new provisions in the field of housing and communal services, aimed at improving economic efficiency in terms of electricity consumption, it becomes very important to ensure its accurate and operational accounting with the possibility of further forecasting of electricity consumption and the state of power grid facilities, which will allow specialized organizations and services, as well as the managing bodies in the shortest time to make a balanced specialized decisions This paper proposes the concept of intelligent control system to manage the process of condition monitoring based on data from intelligent sensors. The novelty of the concept is to consider a variant of solving the problem of integration of information systems associated with weakly structured subject-oriented information flows in the electric power industry enterprise by using methods of set theory and category theory.

Rule and Exemplar-based Transfer in Category Learning.

We compared the neural systems involved in transfer to novel stimuli via rule application versus exemplar processing. Participants learned a categorization task involving abstraction of a complex rule and then categorized different types of transfer stimuli without feedback. Rule stimuli used new features and therefore could only be categorized using the rule. Exemplar stimuli included only one of the features necessary to apply the rule and therefore required participants to categorize based on similarity to individual previously learned category members. Consistent and inconsistent stimuli were formed so that both the rule and feature similarity indicated the same category (consistent) or opposite categories (inconsistent). We found that all conditions eliciting rule-based transfer recruited a medial prefrontal-anterior hippocampal network associated with schematic memory. In contrast, exemplar-based transfer recruited areas of the intraparietal sulcus associated with learning and executing stimulus-category mappings along with the posterior hippocampus. These results support theories of categorization that postulate complementary learning and generalization strategies based on schematic and exemplar mechanisms.

Category of quantizations and inverse problem

We introduce a category composed of all quantizations of all Poisson algebras. By the category, we can treat in a unified way the various quantizations for all Poisson algebras and develop a new classical limit formulation. This formulation proposes a new method for the inverse problem, that is, the problem of finding the classical limit from a quantized space. Equivalence of quantizations is defined by using this category, and the conditions under which the two quantizations are equivalent are investigated. Two types of classical limits are defined as the limits in the context of category theory, and they are determined by giving a sequence of objects. Using these classical limits, we discuss the inverse problem of determining the classical limit from some noncommutative Lie algebra. From a Lie algebra, we construct a sequence of quantized spaces, from which we determine a Poisson algebra. We also present a method to obtain this sequence of quantizations from the principle of least action by using matrix regularization. Apart from the above category of quantizations of all Poisson algebras, a category of quantizations of a fixed single Poisson algebra is also introduced. In this category, the other classical limit is defined, and it is automatically determined for the category.

METHODOLOGY FOR CLASSIFYING MONEY LAUNDERING RISKS TYPOLOGIES

The method of classifying the typologies of money laundering and terrorist financing risks in big data from a variety of data sources of organizational systems is investigated. The main provisions of this technique are theoretically substantiated, reference models and calculation formulas are given. An algebraic approach for the synthesis of the method is proposed, a theoretical justification of the feasibility of its use is given. The algebraic approach to the synthesis of the methodology is implemented on the basis of category theory and the theory of algorithms, in particular the theory of Markov algorithms, which is considered outside of normal algorithms. The N-scheme of the Markov algorithm is considered, which was developed to replace its well-known g-scheme and provides processing of words in natural, artificial and combined languages, which can be represented in an ordered and extended Markov alphabet A±2, which takes into account many sources of big data. Methods for inputting incomplete, heterogeneous (heterogeneous) and non-representative input data samples are given. A method is proposed for converting input data samples into cycles of the Big Data Transfer Protocol. A reference model of the legal economic activity of the organizational system has been synthesized. This reference model is subjected to analysis and signs of illegal economic activity of mutually interacting organizational systems are highlighted. A reference model of the system for classifying the risks of laundering proceeds from crime and financing of terrorism has been developed. To combat money laundering, the N-scheme of the Markov algorithm for one data source and the Markov system, consisting of such schemes, for a variety of big data sources are theoretically substantiated. It is concluded that the synthesized Markov system provides a decomposition of words and their morphisms, contains a common data input control channel, and provides a classification of money laundering risks.

Gapped boundaries of (3+1) -dimensional topological order

Given a gapped boundary of a $(3+1)$-dimensional [$(3+1)\mathrm{D}$] topological order (TO), one can stack on it a decoupled $(2+1)\mathrm{D}$ TO to get another boundary theory. Should one view these two boundaries as ``different''? A natural choice would be no. Different classes of gapped boundaries of $(3+1)\mathrm{D}$ TO should be defined modulo the decoupled $(2+1)\mathrm{D}$ TOs. But is this enough? We examine the possibility of coupling the boundary of a $(3+1)\mathrm{D}$ TO to additional $(2+1)\mathrm{D}$ TOs or fractonic systems, which leads to even more possibilities for gapped boundaries. Typically, the bulk pointlike excitations, when touching the boundary, become excitations in the added $(2+1)\mathrm{D}$ phase, while the stringlike excitations in the bulk may end on the boundary but with end points dressed by some other excitations in the $(2+1)\mathrm{D}$ phase. For a good definition of ``class'' for gapped boundaries of $(3+1)\mathrm{D}$ TO, we choose to quotient out the different dressings as well. We characterize a class of gapped boundaries by the stringlike excitations that can end on the boundary, whatever their end points are. A concrete example is the $(3+1)\mathrm{D}$ bosonic toric code. Using group cohomology and category theory, three gapped boundaries have been found previously: rough boundary, smooth boundary, and twisted smooth boundary. We can construct many more gapped boundaries beyond these, which all naturally fall into two classes corresponding to whether the $m$-string can or cannot end on the boundary. According to this classification, the previously found three boundaries are grouped as {rough}, {smooth, twisted smooth}. For a $(3+1)\mathrm{D}$ TO characterized by a finite group $G$, different classes correspond to different normal subgroups of $G$. We illustrate the physical picture from various perspectives including coupled layer construction, Walker-Wang model, and field theory.

Voltage Lifts of Graphs from a Category Theory Viewpoint

ABSTRACT We prove that the notion of a voltage graph lift comes from an adjunction between the category of voltage graphs and the category of group labeled graphs.

Computational infrastructure for concepts discovery in science and technology

Automated scientific discovery, a topic in artificial intelligence has mainly been used to generate scientific insight from data. Our work follows the knowledge-driven discovery approach and introduces the use of category theory as the foundation for modeling diverse engineering fields represented with combinatorial representation. We show how category theory provides support for all stages of the discovery process starting from modeling the engineering knowledge. We demonstrate the use of the approach to rediscover previous discoveries in mechanics and discover new devices, some of which need to be realized to be appreciated. Category theory allows expanding the process to disciplines not modeled with combinatorial representations. We intend to demonstrate this in future studies.

Development of a Platform for Distributed Energy Resources Management on the Basis of a Digital Twin

The paper discusses the development of a platform for distributed energy resources management based on digital twins. The platform use cases include demand response, electric vehicle charging, peer-to-peer energy trading, storage scheduling, virtual power plant, and so on. Thanks to the digital twin, the platform can perform the use cases controlling either real operation-stage equipment or virtual design-stage simulation models. The platform offers mass distributed energy resources owners and operators to improve the power supply quality (including stability), reduce costs (including transaction overhead), and gain emerging market opportunities (including participation in various aggregators' programs). Software and equipment vendors are interested in the platform's capability to quickly assemble distributed energy management systems almost without programming. The digital twin and the platform are designed with the viewpoint-based approach established by the international systems engineering standard ISO/IEC/IEEE 42010. The typical power system digital twin architecture is described. The major kinds of mathematical models as part of digital twins are presented: physical models based on numerical solutions of differential equations and optimization problems, machine learning models, knowledge-based models. The interoperability of such heterogeneous models is ensured on the basis of the ontological model of distributed energy. The platform architecture is represented from three key viewpoints: functional, information, and software. To formalize and ultimately automate the integration of heterogeneous models, we propose novel mathematical methods of model-based system engineering based on category theory, including universal constructions and the multicomma. The multicomma category is shown to be constructed using standard product, exponent, and pushout constructions, which makes it possible to establish a number of its practically significant properties.