Let $F:\; {\mathscr {C}} \to {\mathscr {E}} \ $ be a functor from a category $\mathscr {C} \ $ to a homological (Borceux–Bourn) or semi-abelian (Janelidze–Márki–Tholen) category $\mathscr {E}$. We investigate conditions under which the homology of an object $X$ in $\mathscr {C}$ with coefficients in the functor $F$, defined via projective resolutions in $\mathscr {C}$, remains independent of the chosen resolution. Consequently, the left derived functors of $F$ can be constructed analogously to the classical abelian case.

Our approach extends the concept of chain homotopy to a non-additive setting using the technique of imaginary morphisms. Specifically, we utilize the approximate subtractions of Bourn–Janelidze, originally introduced in the context of subtractive categories. This method is applicable when $\mathscr {C}$ is a pointed regular category with finite coproducts and enough projectives, provided the class of projectives is closed under protosplit subobjects, a new condition introduced in this article and naturally satisfied in the abelian context. We further assume that the functor $F$ meets certain exactness conditions: for instance, it may be protoadditive and preserve proper morphisms and binary coproducts—conditions that amount to additivity when $\mathscr {C}$ and $\mathscr {E}$ are abelian categories.

Within this framework, we develop a basic theory of derived functors, compare it with the simplicial approach, and provide several examples.

A convex body R in the hyperbolic plane is called reduced if any convex body $K\subset R$ has a smaller minimal width than R. We answer a few of Lassak’s questions about ordinary reduced polygons regarding its perimeter, diameter, and circumradius, and we also obtain a hyperbolic extension of a result of Fabińska.

This article develops an approach to music history that centres performers and their artistic work, drawing on insights from musical performance studies. It responds to criticisms of the practice turn and builds on recent scholarship on Soviet music to contextualize the life of pianist Maria Yudina in the years 1959–63, in which she dedicated herself (at great cost) to new, avant-garde music. Case studies include Yudina’s key role in performing the first Soviet twelve-tone composition in 1961 — Andrei Volkonsky’s Musica Stricta: Fantasia Ricercata — and her advocacy of Igor Stravinsky in the build-up to his homecoming in 1962.

Saponite-like materials have a wide range of potential applications, especially in heterogeneous catalysis. Despite the simplicity of the synthesis, the mechanisms of the formation of saponite are not well understood yet. The aim of the present study was to investigate a possible correlation between the coordination of Al in the solid phase and in the solution. For this, samples were prepared by varying the initial OH:Si molar ratio from 0.18 to 2.14, leading to a pH in the supernatant after the hydrothermal treatment of 6.7 to 12.7, respectively. The characterization of the material was performed by combining nuclear magnetic resonance (NMR) and X-ray absorption near edge structure (XANES) spectroscopies, and good agreement was obtained between the two techniques. Between pH7 and pH10, 60–65% of aluminum was found to be in tetrahedral coordination, while this percentage increased above pH10 (up to 81%). These results correlated with the speciation of the aluminum in aqueous solution. Indeed, above pH10, all available aluminum was in the soluble form Al(OH)4–.

The international recognition of the Armenian genocide is the most prominent issue shaping Turkish-Armenian relations today. Nevertheless, the academic literature lacks empirical analyses of people’s perceptions of the genocide in Turkey. To address the gap, the article provides an exploratory investigation into people’s online comments regarding the genocide on the most popular Turkish forum website, Eksisozluk. Guided by Cohen’s (2001) theoretical approach, the study explores online entries on the topic spanning from 2002 to 2018 (N = 2127). The findings reveal eleven attitudes that individuals adopt in the debate. The article examines the diversity in responses by utilizing Cohen’s typology, which helps to define and categorize individuals’ rationales for denial. Further, it shows that Cohen’s approach could contribute to explaining non-denying responses to the recollection of past suffering. The study concludes that people do not uniformly follow the official line concerning the Armenian genocide in Turkey.

‘Complex emotional needs’ has emerged in the UK as a label to refer to individuals given a diagnosis of a personality disorder. We argue that this name change is insufficient to address the harms associated with the personality disorder construct; rather, it risks broadening its scope, and thereby the construct’s harms.

This essay reflects on a new digital realization by Andrew Hugill of the ‘Christian ballet’ Uspud (1892) by Erik Satie and J. P. Contamine de Latour. The creative process of making the realization entailed a critical re-examination of existing scholarship and revealed that the relationship between music and drama is closer than has previously been understood. The essay situates Uspud in the context of 1890s Montmartre and demonstrates beyond reasonable doubt that it was conceived as a shadow play and scored for solo harmonium. It analyses the music in detail, considering how its motivic construction and use of timbral contrasts both supports the action and conveys the inner states of uspud himself. It considers the humorous and serious aspects of Uspud, arguing that this was a key work in the evolution of Satie’s artistic and personal identity.

Let $e$ and $q$ be fixed co-prime integers satisfying $1\lt e\lt q$. Let $\mathscr {C}$ be a certain family of deformations of the curve $y^e=x^q$. That family is called the $(e,q)$-curve and is one of the types of curves called plane telescopic curves. Let $\varDelta$ be the discriminant of $\mathscr {C}$. Following pioneering work by Buchstaber and Leykin (BL), we determine the canonical basis $\{ L_j \}$ of the space of derivations tangent to the variety $\varDelta =0$ and describe their specific properties. Such a set $\{ L_j \}$ gives rise to a system of linear partial differential equations (heat equations) satisfied by the function $\sigma (u)$ associated with $\mathscr {C}$, and eventually gives its explicit power series expansion. This is a natural generalisation of Weierstrass’ result on his sigma function. We attempt to give an accessible description of various aspects of the BL theory. Especially, the text contains detailed proofs for several useful formulae and known facts since we know of no works which include their proofs.

The rising incidence of neurodegenerative diseases in an ageing global population has shifted research focus towards modifiable risk factors, such as diet. Despite potential links between dietary patterns and brain health, inconsistencies in neuroimaging outcomes underscore a gap in understanding how diet impacts brain ageing. This study explores the relationship between three dietary patterns – Mediterranean, Dietary Approaches to Stop Hypertension (DASH) and Mediterranean-DASH Intervention for Neurodegenerative Delay – and cognitive outcomes as well as brain connectivity. The study aimed to assess the association of these diets with brain structure and cognitive function, involving a middle-aged healthy group and an older cohort with subjective cognitive decline. The study included cognitive assessments and diffusion-weighted MRI data to analyse white matter microstructural integrity. Participants comprised fifty-five older individuals with subjective cognitive decline (54·5 % female, mean age = 64) and fifty-two healthy middle-aged individuals (48·1 % female, mean age = 53). Age inversely correlated with certain cognitive functions and global brain metrics, across both cohorts. Adherence to the Mediterranean, DASH and Mediterranean-DASH Intervention for Neurodegenerative Delay diets showed no significant cognitive or global brain metric improvements after adjusting for covariates (age, education, BMI). Network-based statistics analysis revealed differences in brain subnetworks based on DASH diet adherence levels in the subjective cognitive decline cohort. In the healthy cohort, lower white matter connectivity was associated with reduced adherence to Mediterranean-DASH Intervention for Neurodegenerative Delay and DASH diets. Ultimately, the study found no strong evidence connecting dietary patterns to cognitive or brain connectivity outcomes. Future research should focus on longitudinal studies and refine dietary assessments.

Throughout the Cold War, Yugoslavia was the only socialist country that participated in the Western-led international refugee regime and acted as a transit zone for refugees hoping to reach the Western Bloc. Those transiting were mainly, but not exclusively, escapees from various countries in the Soviet bloc. A few refugee groups also settled in Yugoslavia against the backdrop of shifts in international constellations, tense relationships with neighboring countries, and transnational mobilizations. This article will first investigate the dichotomy between transit and the few instances of refugees integrating into socialist Yugoslavia. Next, it will investigate the ease of the resettlement process by exploring how the length of time spent in the country was influenced by hierarchies among different refugee groups based on ethnic origin, political allegiances, class, and which opportunities for resettlement were available to whom. Finally, it will reflect on how the changing role of temporary refuge or permanent haven that Yugoslavia ascribed to itself was constructed and challenged by the host society, potential countries of resettlement, and the refugees themselves.

This article is an outcome of a search for the Tamil plantation woman in Malaysia and her voice—her stories and memories, in her own words. Through the plantation songs of Tamil workers in Malaysia, first collated and published in the 1980s, we explore the experiences and memories of these women, singing about their lives and work in the Malayan plantations. As memory-work, these songs constitute an oral history that provides an uneasy counter to hegemonic discourses like that of the colonial planters who employed the women, or the nationalist historiography of India and Malaysia where they are sidelined and reduced to figures of abject victimhood in the clutches of colonial capitalism, or the post-colonial discourse where their memories and experiences constitute a shameful past that obstructs optimism for the future. Tamil plantation songs call for a comparative approach to history and memory—between the position of the woman and that of the man, or the labourer and the supervisor/planter, as well as more problematic and shifting positionalities like seducer and the seduced, or the victim and the perpetrator.

This article explores the development of the Safari Rally in the context of intertwined trends in mobility, sports, and consumerism at local, global and intermediate levels. The first section briefly presents the Safari Rally. The second section discusses the significance and development of the sport of rallying in the context of global automobility and changes in the motor industry, highlighting in particular the professionalisation of sport and the forces driving it. The third section analyses why the Safari became relevant to so many stakeholders in Africa and across the globe, and how these shaped its development from its colonial origins through decolonisation and beyond. Highlighting the factors accounting for the rise, and decline, of the Safari as a sporting event of global significance contributes to understanding how mobility, sports, and consumerism were interlinked across continents in the second half of the 20th century.

The Habsburg Empire has typically been understood as a continental power with few overseas aspirations, or as Robert Musil waxed nostalgically in his fictional Kakania: “A Ship would now and then be sent off to South America or East Asia, but not too often.” It is mostly true, of course, that Austria did not have “ambition for world markets or world power,”1 but recently historians have begun to explore the role colonial fantasy played in an empire with no actual overseas colonies to speak of.2 The Empire did support a series of oceanic voyages in the 19th century. None resulted in permanent settlement of course, but the voracious enthusiasm with which a Habsburg public responded to them is a testament to the weight colonial discourse had even in continental empires like Austria's.3 A small, but exciting literature has sprung up around these expeditions, situating them in their broader political contexts.4 The exercise has been fruitful at situating Habsburg history in a broader global context and has done much to de-provincialize what was once a relatively insular field.