Category Theory Research Articles

기업가정신 이론과 연구 프로그램

Entrepreneurship has been attained the legitimacy and growth for the proactive engagement of diverse fields. Entrepreneurship theories encompass various aspects of complex phenomenon. However, the theoretical development is weak to explain the complex phenomenon to use in the field(Who cares?). Startup and Scale entrepreneurship are distinctive from ordinary administration for the uncertainty, innovation, and unknown market. The entrepreneurial process has ‘emerged’ from complex and particular reality and human conditions. So we have research opportunities for further theoretical development including meta theorizing according to the Academic Progress Taxonomy(APT). The APT has TREE category(Theory building, Research methods, Exemplar, Evidence). Entrepreneurship inherited multi-disciplinary theoretical resources and challenges to figure out the meta-theory. With more integrative and extendable meta-theory, we could taste salt of ocean is emergence based on entrepreneurity. An integrative multi-layered framework is an emergence-based meta-theory: COSANE (Customer, Organizational, Social, Natural, Economic) value layer above the Scale-up layer(Opportunities, Competence, Ecosystem, Advancement, and Network) and Startup layer(Orientation, Cognition, Entrepreneurity, Action, Novelty) layer. Research programs are proposed according to the OCEANS framework with vertical(upward/downard) and horizontal causation and new combinations of research methods. More research agendas are discussed.

Shared Protentions in Multi-Agent Active Inference.

In this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory in mathematics to develop a comprehensive framework for understanding social action premised on shared goals. We begin with an overview of Husserlian phenomenology, focusing on aspects of inner time-consciousness, namely, retention, primal impression, and protention. We then review active inference as a formal approach to modeling agent behavior based on variational (approximate Bayesian) inference. Expanding upon Husserl's model of time consciousness, we consider collective goal-directed behavior, emphasizing shared protentions among agents and their connection to the shared generative models of active inference. This integrated framework aims to formalize shared goals in terms of shared protentions, and thereby shed light on the emergence of group intentionality. Building on this foundation, we incorporate mathematical tools from category theory, in particular, sheaf and topos theory, to furnish a mathematical image of individual and group interactions within a stochastic environment. Specifically, we employ morphisms between polynomial representations of individual agent models, allowing predictions not only of their own behaviors but also those of other agents and environmental responses. Sheaf and topos theory facilitates the construction of coherent agent worldviews and provides a way of representing consensus or shared understanding. We explore the emergence of shared protentions, bridging the phenomenology of temporal structure, multi-agent active inference systems, and category theory. Shared protentions are highlighted as pivotal for coordination and achieving common objectives. We conclude by acknowledging the intricacies stemming from stochastic systems and uncertainties in realizing shared goals.

Green or greenwashed? Examining consumers' ability to identify greenwashing

Nowadays, companies and consumers face the challenge of navigating around the pitfalls of greenwashing in markets presenting uncountable new and existing green products. This research examines consumer perceptions of such products and the extent to which consumers are able to identify greenwashing. Drawing on categorization theory, consumers may classify a new product based on different green cues as honest green, greenwashed, or non-green. We test this ability across three different products in two experimental studies (N = 700) conducted in Germany and find that consumers fall for greenwashing when they are asked solely for their purchase intentions. Activating a greenwashed product category by asking participants for their perceived greenwashing helped them to spot the differences between the green products. This research contributes to the literature by directly examining consumers' ability to distinguish between greenwashed and honest green products and by providing empirical evidence that consumers can do so when they are primed. That is, the activation of a greenwashed product category can support consumers in identifying greenwashing. Practically speaking, this research may point public policy toward category activation as a simple measure to help consumers unmask greenwashing in purchase contexts.

Gauging non-invertible symmetries: topological interfaces and generalized orbifold groupoid in 2d QFT

Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it connects distinct theories and also reveals hidden structures in a given theory. We initiate a systematic investigation of gauging discrete generalized symmetries in two-dimensional QFT. Such symmetries are described by topological defect lines (TDLs) which obey fusion rules that are non-invertible in general. Despite this seemingly exotic feature, all well-known properties in gauging invertible symmetries carry over to this general setting, which greatly enhances both the scope and the power of gauging. This is established by formulating generalized gauging in terms of topological interfaces between QFTs, which explains the physical picture for the mathematical concept of algebra objects and associated module categories over fusion categories that encapsulate the algebraic properties of generalized symmetries and their gaugings. This perspective also provides simple physical derivations of well-known mathematical theorems in category theory from basic axiomatic properties of QFT in the presence of such interfaces. We discuss a bootstrap-type analysis to classify such topological interfaces and thus the possible generalized gaugings and demonstrate the procedure in concrete examples of fusion categories. Moreover we present a number of examples to illustrate generalized gauging and its properties in concrete conformal field theories (CFTs). In particular, we identify the generalized orbifold groupoid that captures the structure of fusion between topological interfaces (equivalently sequential gaugings) as well as a plethora of new self-dualities in CFTs under generalized gaugings.

Internal sums for synthetic fibered (∞,1)-categories

We give structural results about bifibrations of (internal) (∞,1)-categories with internal sums. This includes a higher version of Moens' Theorem, characterizing cartesian bifibrations with extensive aka stable and disjoint internal sums over lex bases as Artin gluings of lex functors. We also treat a generalized version of Moens' Theorem due to Streicher which does not require the Beck–Chevalley condition. Furthermore, we show that also in this setting the Moens fibrations can be characterized via a condition due to Zawadowski.Our account overall follows Streicher's presentation of fibered category theory à la Bénabou, generalizing the results to the internal, higher-categorical case, formulated in a synthetic setting. Namely, we work inside simplicial homotopy type theory, which has been introduced by Riehl and Shulman as a logical system to reason about internal (∞,1)-categories, interpreted as Rezk objects in any given Grothendieck–Rezk–Lurie (∞,1)-topos.

Product categorization of Korean rice wine (makgeolli) compared to beer and wine using sensory evaluation methods

AbstractThis study aims to investigate the product categorization and characterization of makgeolli (Korean rice wine [KRW]) among beer and wine samples. Projective mapping with ultra‐flash profiling (PM with UFP) (n = 68) was conducted with 12 alcoholic beverage samples, including wines, beers, and makgeolli, and showed that participants characterized wine based on fruitiness, beer on bitterness, and makgeolli on sourness. s showed that PM with UFP had a combined explained variance of 47.4% with beer, wine, and makgeolli grouped separately. However, when participants were separated based on wine knowledge, low wine knowledge participants placed Shiraz close to makgeolli indicating participants were using a different metric in grouping the alcoholic beverage samples. When participants were tasked with using polarized sensory positioning (n = 91) to characterize makgeolli and wines, participants regardless of wine knowledge showed that wine and makgeolli had unique sensory traits and thus should be categorized differently.Practical ApplicationsResearch on KRW (makgeolli) is relatively limited in Western societies and this study attempts to understand how participants categorize makgeolli in New Zealand among different alcoholic beverages using projective and characterizing methods. Based on the categorization theory, it is important to position the product properly in the food and beverage categories as consumers may use the category cues to evaluate makgeolli and use products such as beer or wine within the same category as price anchors for makgeolli's price in the market. The results showed that participants categorize makgeolli differently compared to wine and beer; therefore, it would be beneficial to position makgeolli separately. Practical applications may include creating a separate section on a restaurant beverage menu, a webpage on an alcoholic beverage seller's website, or a small sub‐section on the retail store shelf. Placing makgeolli in the wine section as previously suggested is not recommended.

Think star, think men? Implicit star performer theories

SummaryThe star performer gender gap highlights women's challenges in being recognized as star performers. We investigated whether people hold shared beliefs about characteristics star performers possess (i.e., implicit star performer theories, ISPTs) and whether perceptions of stars are (a) gendered and (b) context‐specific. Guided by categorization theory, we argue that individuals have shared perceptions of what constitutes a star performer. Employing an inductive approach, we uncovered the existence of ISPTs that are distinct and differ from previously identified implicit theories, such as those about leadership. Specifically, stars were believed to have six characteristics: Driven, Relational, Extraordinary, Fascinating, Tenacious, and Brilliant. We then applied role congruity theory to argue that perceptions of star performers would be gendered and context‐dependent. Using an experimental approach, we ascertained that people associated star performers with more masculine than feminine attributes, what we labeled the think star, think men phenomenon. Moreover, this association was context‐dependent, such that the association of star performers with masculine attributes was stronger in men‐dominated occupations. Our third study used a non‐reactive approach (i.e., “Princeton trilogy”), and results showed that star performers are seen as possessing more masculine attributes than very good employees. Overall, our three studies using inductive, experimental, and indirect methods based on eight samples of 2322 participants consistently supported the existence of ISPTs and the think star, think men phenomenon, improving our understanding of the star performer gender gap.

Category theory as a mathematical framework in spatial analysis; Challenges and opportunities

Category theory as a mathematical framework in spatial analysis; Challenges and opportunities

Describing Translation Techniques Used in the Translation of Culturally Bound Terms in West Java Calendar of Event 2020

This research aims at analyzing translation techniques used by the translator in translating the booklet "West Java Calendar of Event 2020" from Indonesian into English. This booklet is published by the Department of Tourism and Culture, West Java. Specifically, this research highlights the translation of culturally bound terms in the booklet. The researchers are interested in analyzing this topic because cultural-bound terms are considered challenging to translate; the translators must understand the cultural background of the languages they are translating. Moreover, it is not likely that translators can find one-to-one correspondence for each cultural term in the text. This study applies a descriptive qualitative method since the data are in the form of text and the researchers also play a role as the key instrument in collecting the data, in this case through document examination. In this research, total sampling technique is applied since the researchers take all of the culturally bound terms in the booklet. The research begins with collecting the cultural terms from the booklet, classifying them into cultural terms categories based on Newmark’s theory of cultural category, and determining the translation techniques based on Molina and Albir’s theory. The result shows that the translator mainly employs borrowing, amplification, description, and established equivalent techniques. There is a tendency that the translator prefers those techniques because it is hard for the translator to find one-to-one correspondence of the terms in the target language. Hopefully, this research will be beneficial for translators in deciding the proper translation techniques in translating cultural terms.

The impact of discrimination on the psychological wellbeing and ethnic identity of international students in North Cyprus

The social categorization theory suggests that ingroup bias is a common cognitive bias that can result in discrimination against outgroup members. In recent years there has been a notable increase in the international student body globally as well as an increase in the diversity of the students. Considering this background, it is imperative to investigate the social experiences of this group of students. The current research investigates experiences of discrimination among international students and how they influence their ethnic identity and psychological well-being. A sample of 386 students was recruited from 2 universities in Northern Cyprus using a convenience sampling technique. The findings show a positive relationship between discrimination and psychological distress. The findings also show that ethnic identity is negatively correlated with discrimination and psychological distress. International students who reported higher scores of discrimination showed higher levels of stress and depression. This is because discrimination would result in social exclusion or isolation. High levels of discrimination are associated with low ethnic identity scores among international students. The study shows that ethnic identity does not mediate the impact of discrimination on psychological well-being (psychological distress, depression, anxiety, stress). The findings also show that there are significant differences in discrimination based on race and religion this may be linked to cultural distance between the host and home countries. Considering these findings, educational institutions should increase support services offered to international students, offer awareness and sensitivity training for multicultural interactions and, also incorporate authentic sustainability curricula.

상사는 부하의 피드백 추구행동을 어떻게 볼까?: 피드백 추구행동이 유능함 인식과 성과평가에 미치는 영향에서 주체 지향성의 조절역할

The answer to how a subordinate's feedback seeking behavior will be deemed by supervisor
 is a significant motivational factor that influence employees' feedback seeking. It is also
 essential for organizations to organize policies that encourage feedback seeking behavior.
 Based on the theories of similarity-attraction, social categorization, and social identity, this
 study argues whether supervisor's agentic orientation is high or low, feed seeking behavior
 will positively or negatively influence perception of subordinate's competence. Furthermore,
 this study suggests the interaction effect of feedback seeking behavior and agentic orientation
 will influence performance evaluation via perceived competence. To test the hypotheses,
 path analysis using Mplus 8 was conducted based on data from 210 pairs of supervisorsemployees
 in military settings. The result revealed that the relationship between feedback seeking
 behavior and perceived competence was moderated by agentic orientation. Specifically, when
 supervisors had high agentic orientation, there was a significant positive relationship between
 two variables. However, when supervisors had low agentic orientation, there was no significant
 relationship. Perceived competence mediated the interaction effect of feedback seeking behavior
 and agentic orientation. This study contributes to the literature by examining how feedback
 seeking behavior is interpreted from a supervisor's perspective, going beyond the traditional
 employee-focused perspective. Additionally, it offers practical implications for organizational
 managers in terms of human resource management.

Interpretative Flexibility of Digital Immigrant Towards Ajaib Stock Trading Application

The Digital Immigrant as users of financial technology, particularly Ajaib Stock Application represent a group that has witnessed the inception and evolution of digital technology, typically lacking proficiency in operating modern technological tools. This study aims to uncover the interpretative flexibility of Digital Immigrants in their experience of using the Ajaib application. The research is grounded in the Social Construction of Technology theory, Phenomenological theory, and Social Category theory. The paradigm of this research adopting a constructivist, the research approach using a qualitative approach, utilizing phenomenological research methods. Data collection techniques used in this study by semi-structured interviews and literature studies. The study reveals that Digital Immigrants demonstrate interpretative flexibility in navigating the Ajaib application amidst the challenges posed by the Covid-19 pandemic. The diversity of interpretative flexibility is based on the various initial motives for using the application, categorized into motives 'because of' and 'in order to'. These motives influence interpretative flexibility concerning language, usage, and structure. Additionally, the interpretative flexibility of digital immigrants is intertwined with a wider context, reflecting various challenges encountered while engaging with the Ajaib application.

Conjecturing is not all

Although generating empirically grounded theoretical contributions has been an essential aim of design research from the beginning, the underlying methodology has been described as in need for further elaboration with respect to rigor. Existing methodological elaborations on theorizing in design research often focus on argumentative grammar of strengthening prescriptive conjectures. Beyond these, this paper argues that prescriptive theory elements require generating categorial, descriptive, and explanatory theory elements before the suggested argumentative grammars can be treated. With an example from a design research study for professional development, the immense work of elaborating categorial and explanatory theory elements is illustrated that is needed before concise prescriptive conjectures can be made and tested.

Separable MV-algebras and lattice-ordered groups

The theory of extensive categories determines in particular the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product of algebras of rational numbers—i.e., of subalgebras of the MV-algebra [0,1]∩Q. Beyond its intrinsic algebraic interest, this research is motivated by the long-term programme of developing the algebraic geometry of the opposite of the category of MV-algebras, in analogy with the classical case of commutative K-algebras over a field K.

Anomaly enforced gaplessness and symmetry fractionalization for SpinG symmetries

Symmetries and their anomalies give strong constraints on renormalization group (RG) flows of quantum field theories. Recently, the identification of a theory’s global symmetries with its topological sector has provided additional constraints on RG flows to symmetry preserving gapped phases due to mathematical results in category and topological quantum field theory. In this paper, we derive constraints on RG flows from ℤ2-valued pure- and mixed-gravitational anomalies that can only be activated on non-spin manifolds. We show that such anomalies cannot be matched by a unitary, symmetry preserving gapped phase without symmetry fractionalization. In particular, we discuss examples that commonly arise in 4d gauge theories with fermions.

A category theory approach to the semiotics of machine learning

A category theory approach to the semiotics of machine learning

The Structure of Meaning in Language: Parallel Narratives in Linear Algebra and Category Theory

The Structure of Meaning in Language: Parallel Narratives in Linear Algebra and Category Theory

Operads, Operadic Categories and the Blob Complex

We will show that the Morrison–Walker blob complex appearing in Topological Quantum Field Theory is an operadic bar resolution of a certain operad composed of fields and local relations. As a by-product we develop the theory of unary operadic categories and study some novel and interesting phenomena arising in this context.

Musical experience is linked to enhanced dimension-selective attention to pitch and increased primary weighting during suprasegmental categorization.

Speech perception requires the integration of evidence from acoustic cues across multiple dimensions. Individuals differ in their cue weighting strategies, that is, the weight they assign to different dimensions during speech categorization. In two experiments, we investigate musical training as one potential predictor of individual differences in prosodic cue weighting strategies. Attentional theories of speech categorization suggest that prior experience with the task-relevance of a particular dimension leads that dimension to attract attention. Experiment 1 tested whether musicians and nonmusicians differed in their ability to selectively attend to pitch and loudness in speech. Compared to nonmusicians, musicians showed enhanced dimension-selective attention to pitch but not loudness. Experiment 2 tested the hypothesis that musicians would show greater pitch weighting during prosodic categorization due to prior experience with the task-relevance of pitch cues in music. Listeners categorized phrases that varied in the extent to which pitch and duration signaled the location of linguistic focus and phrase boundaries. During linguistic focus categorization, musicians upweighted pitch compared to nonmusicians. During phrase boundary categorization, musicians upweighted duration relative to nonmusicians. These results suggest that musical experience is linked with domain-general enhancements in the ability to selectively attend to certain acoustic dimensions in speech. As a result, musicians may place greater perceptual weight on a single primary dimension during prosodic categorization, while nonmusicians may be more likely to choose a perceptual strategy that integrates across multiple dimensions. These findings support attentional theories of cue weighting, which suggest attention influences listeners' perceptual weighting of acoustic dimensions during categorization. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Auslander–Reiten theory in extriangulated categories

The notion of an extriangulated category gives a unification of existing theories in exact or abelian categories and in triangulated categories. In this article, we develop Auslander–Reiten theory for extriangulated categories. This unifies Auslander–Reiten theories developed in exact categories and triangulated categories independently. We give two different sets of sufficient conditions on the extriangulated category so that existence of almost split extensions becomes equivalent to that of an Auslander–Reiten–Serre duality. We also show that existence of almost split extensions is preserved under taking relative extriangulated categories, ideal quotients, and extension-closed subcategories. Moreover, we prove that the stable category C _ \underline {\mathscr {C}} of an extriangulated category C \mathscr {C} is a τ \tau -category (see O. Iyama [Algebr. Represent. Theory 8 (2005), pp. 297–321]) if C \mathscr {C} has enough projectives, almost split extensions and source morphisms. This gives various consequences on C _ \underline {\mathscr {C}} , including Igusa–Todorov’s Radical Layers Theorem (see K. Igusa and G. Todorov [J. Algebra 89 (1984), pp. 105–147]), Auslander–Reiten Combinatorics on dimensions of Hom-spaces, and Reconstruction Theorem of the associated completely graded category of C _ \underline {\mathscr {C}} via the complete mesh category of the Auslander–Reiten species of C _ \underline {\mathscr {C}} . Finally we prove that any locally finite symmetrizable τ \tau -quiver (=valued translation quiver) is an Auslander–Reiten quiver of some extriangulated category with sink morphisms and source morphisms.