title: On D-inverse constellations: An alternative view of ordered groupoids

authors: Hughes, Kaden

abstract: A groupoid is a category in which every arrow has an inverse. The ESN (Ehresmann-Schein-Nambooripad) theorem states that the category of inverse semigroups is isomorphic to the category of inductive groupoids, which are groupoids with additional order-theoretic structure. Inductive groupoids are special types of ordered groupoids; the latter shares most of the properties of inductive groupoids but do not correspond to any type of semigroup. Despite this, many of the main facts about inverse semigroups carry over to ordered groupoids, and ordered groupoids have been shown to be an important tool in the study of inverse semigroups. Since then, it has been found that a particular type of partial algebra we call D-inverse constellations are equivalent to ordered groupoids, but have an arguably simpler, purely algebraic definition. This thesis will explore and illustrate the value of working with D-inverse constellations rather than ordered groupoids, presenting an alternative formulation and proof of the ESN Theorem using D-inverse constellations.

text: On D-inverse constellations: An alternative view of ordered groupoids A groupoid is a category in which every arrow has an inverse. The ESN (Ehresmann-Schein-Nambooripad) theorem states that the category of inverse semigroups is isomorphic to the category of inductive groupoids, which are groupoids with additional order-theoretic structure. Inductive groupoids are special types of ordered groupoids; the latter shares most of the properties of inductive groupoids but do not correspond to any type of semigroup. Despite this, many of the main facts about inverse semigroups carry over to ordered groupoids, and ordered groupoids have been shown to be an important tool in the study of inverse semigroups. Since then, it has been found that a particular type of partial algebra we call D-inverse constellations are equivalent to ordered groupoids, but have an arguably simpler, purely algebraic definition. This thesis will explore and illustrate the value of working with D-inverse constellations rather than ordered groupoids, presenting an alternative formulation and proof of the ESN Theorem using D-inverse constellations.

year: 2024-04-13

title: Summer of Euphony

authors: Lodge, Martin

abstract: This is a contribution included in the book ‘Jack! Celebrating Jack Body, Composer’. A book which celebrates the life and work of Jack Body through the recollections of friends and colleagues.

text: Summer of Euphony This is a contribution included in the book ‘Jack! Celebrating Jack Body, Composer’. A book which celebrates the life and work of Jack Body through the recollections of friends and colleagues.

year: 2015

title: Māori men: An indigenous psychological perspective on the interconnected self

authors: Rua, Mohi

subjects: Māori men

abstract: The positive relational practices of Māori men are seldom explored in academic research. Responding to this gap in the literature, this article explores how Māori men negotiate a positive sense of self and relationships. This research is guided by kaupapa Māori research practice, Māori cultural concepts, and relational understandings of identity and wellbeing. Our ethnographic approach involved direct observations, engagement in shared cultural practices and narrative interviews. During these interactions, participating men invoked a positive sense of self through accounts of belonging, reciprocity, dialogue, intimacy, and care for themselves, their whānau, and traditions. We found that Māori men's identities are negotiated through interactions with whānau (immediate and extended family), and particular places and practices. Our participants demonstrated how Māori men’s positive self-constructions are fundamentally interconnected with other people, cultural traditions, socio-cultural practices, physical and symbolic places, as well as their own health and the health of those around them.

text: Māori men: An indigenous psychological perspective on the interconnected self The positive relational practices of Māori men are seldom explored in academic research. Responding to this gap in the literature, this article explores how Māori men negotiate a positive sense of self and relationships. This research is guided by kaupapa Māori research practice, Māori cultural concepts, and relational understandings of identity and wellbeing. Our ethnographic approach involved direct observations, engagement in shared cultural practices and narrative interviews. During these interactions, participating men invoked a positive sense of self through accounts of belonging, reciprocity, dialogue, intimacy, and care for themselves, their whānau, and traditions. We found that Māori men's identities are negotiated through interactions with whānau (immediate and extended family), and particular places and practices. Our participants demonstrated how Māori men’s positive self-constructions are fundamentally interconnected with other people, cultural traditions, socio-cultural practices, physical and symbolic places, as well as their own health and the health of those around them.

year: 2017