title: Constellations and their relationship with categories

authors: Gould, Victoria

subjects: mathematics

abstract: Constellations are partial algebras that are one-sided generalisations of categories. Indeed, we show that a category is exactly a constellation that also satisfies the left-right dual axioms. Constellations have previously appeared in the context of inductive constellations: the category of inductive constellations is known to be isomorphic to the category of left restriction semigroups. Here we consider constellations in full generality, giving many examples. We characterise those small constellations that are isomorphic to constellations of partial functions. We examine in detail the relationship between constellations and categories. In particular, we characterise those constellations that arise as (sub-)reducts of categories. We demonstrate that the notion of substructure can be captured within constellations but not within categories. We show that every constellation P gives rise to a category (Formula presented.), its canonical extension, in a simplest possible way, and that P is a quotient of (Formula presented.) in a natural sense. We also show that many of the most common concrete categories may be constructed from simpler quotient constellations using this construction. We characterise the canonical congruences (Formula presented.) on a given category (Formula presented.) (those for which (Formula presented.), and show that the category of constellations is equivalent to the category of (Formula presented.)-categories, that is, categories equipped with distinguished canonical congruence (Formula presented.). The main observation of this paper is that category theory as it applies to the familiar concrete categories of modern mathematics (which come equipped with natural notions of substructures and indeed are (Formula presented.)-categories) may be subsumed by constellation theory.

text: Constellations and their relationship with categories Constellations are partial algebras that are one-sided generalisations of categories. Indeed, we show that a category is exactly a constellation that also satisfies the left-right dual axioms. Constellations have previously appeared in the context of inductive constellations: the category of inductive constellations is known to be isomorphic to the category of left restriction semigroups. Here we consider constellations in full generality, giving many examples. We characterise those small constellations that are isomorphic to constellations of partial functions. We examine in detail the relationship between constellations and categories. In particular, we characterise those constellations that arise as (sub-)reducts of categories. We demonstrate that the notion of substructure can be captured within constellations but not within categories. We show that every constellation P gives rise to a category (Formula presented.), its canonical extension, in a simplest possible way, and that P is a quotient of (Formula presented.) in a natural sense. We also show that many of the most common concrete categories may be constructed from simpler quotient constellations using this construction. We characterise the canonical congruences (Formula presented.) on a given category (Formula presented.) (those for which (Formula presented.), and show that the category of constellations is equivalent to the category of (Formula presented.)-categories, that is, categories equipped with distinguished canonical congruence (Formula presented.). The main observation of this paper is that category theory as it applies to the familiar concrete categories of modern mathematics (which come equipped with natural notions of substructures and indeed are (Formula presented.)-categories) may be subsumed by constellation theory.

year: 2017

title: Employee Perceptions of Fit, Intention to Quit, Organizational Commitment, Job Satisfaction and Work Engagement: Direct, Mediation and Moderation Effects

authors: Amerasinghe, Inakshie

subjects: Person-Environment Fit

abstract: This research examined important work related perceptions and attitudes of employees currently working across major industries in New Zealand to gain insight into factors, including person-environment fit and intention to quit, that could contribute to the overall success of an organization, and the well-being of individuals at work.
The research model consisted of three parts: part A examined employee fit perceptions, namely value congruence, demands-abilities fit and needs-supplies fit, in direct relation to intention to quit.  Part B proposed that the direct relationships predicted in part A would be mediated by organizational commitment, job satisfaction and work engagement.  Part C proposed that work-related attitudes (continuance commitment and job satisfaction) and employee perceptions (needs-supplies fit) would moderate the relationships between types of perceived fit and employee intention to quit.
Two hundred and two surveys were included in the data analyses which showed complete support for the relationships predicted in part A and B of the theoretical model.  Of the three fit types investigated in this study, it was found that needs-supplies fit had the strongest correlation with employee intention to quit.  A few other key findings were that affective commitment mediated the relationship between value congruence and intention to quit, and that both job satisfaction and work engagement mediated the relationship between demands-abilities fit and intention to quit.  No support was found for part C (moderated relationships).  Although no causal inferences should be drawn from these results, these findings highlight the importance of employee fit perceptions, by demonstrating how types of fit can impact upon an employee’s intention to quit both directly and indirectly through work-attitudes.
A major implication that can be drawn from this research is that business owners could benefit from focusing specifically on certain essential types of P-E fit during the recruitment and selection process by selecting future employees with personal values that align with the values of the organization, have abilities to match the demands of the job role and have needs that can be matched by the supplies an organization has to offer. Continually monitoring the fit perceptions and attitudes of current employees through the application of feedback systems is also encouraged.  Focusing on such factors provides employers with the opportunity to manage work-related perceptions and attitudes of employees in order to establish a healthy work-environment.

text: Employee Perceptions of Fit, Intention to Quit, Organizational Commitment, Job Satisfaction and Work Engagement: Direct, Mediation and Moderation Effects This research examined important work related perceptions and attitudes of employees currently working across major industries in New Zealand to gain insight into factors, including person-environment fit and intention to quit, that could contribute to the overall success of an organization, and the well-being of individuals at work.
The research model consisted of three parts: part A examined employee fit perceptions, namely value congruence, demands-abilities fit and needs-supplies fit, in direct relation to intention to quit.  Part B proposed that the direct relationships predicted in part A would be mediated by organizational commitment, job satisfaction and work engagement.  Part C proposed that work-related attitudes (continuance commitment and job satisfaction) and employee perceptions (needs-supplies fit) would moderate the relationships between types of perceived fit and employee intention to quit.
Two hundred and two surveys were included in the data analyses which showed complete support for the relationships predicted in part A and B of the theoretical model.  Of the three fit types investigated in this study, it was found that needs-supplies fit had the strongest correlation with employee intention to quit.  A few other key findings were that affective commitment mediated the relationship between value congruence and intention to quit, and that both job satisfaction and work engagement mediated the relationship between demands-abilities fit and intention to quit.  No support was found for part C (moderated relationships).  Although no causal inferences should be drawn from these results, these findings highlight the importance of employee fit perceptions, by demonstrating how types of fit can impact upon an employee’s intention to quit both directly and indirectly through work-attitudes.
A major implication that can be drawn from this research is that business owners could benefit from focusing specifically on certain essential types of P-E fit during the recruitment and selection process by selecting future employees with personal values that align with the values of the organization, have abilities to match the demands of the job role and have needs that can be matched by the supplies an organization has to offer. Continually monitoring the fit perceptions and attitudes of current employees through the application of feedback systems is also encouraged.  Focusing on such factors provides employers with the opportunity to manage work-related perceptions and attitudes of employees in order to establish a healthy work-environment.

year: 2014

title: Connections, working collaboratively and health workforce development

authors: Masters-Awatere, Bridgette

subjects: Rangahau Māori

abstract: I was invited to deliver a presentation as part of the Inaugral series of research symposia hosted by the national Maori health authority - Te Aka Whaiora

text: Connections, working collaboratively and health workforce development I was invited to deliver a presentation as part of the Inaugral series of research symposia hosted by the national Maori health authority - Te Aka Whaiora

year: 2023-08-30