Tensor products of finitely cocomplete and abelian categories

The purpose of this article is to study the existence of Deligne's tensor product of abelian categories by comparing it with the well-known ten- sor product of finitely cocomplete categories. The main result states that the former exists precisely when the latter is an abelian category, and moreover in this case both tensor products coincide. An example of two abelian categories whose Deligne tensor product does not exist is given.Comment: 14 page

Lax orthogonal factorisation systems

This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections studied by Cassidy, H\'ebert and Kelly. Each simple 2-monad on a finitely complete 2-category gives rise to a lax orthogonal algebraic weak factorisation system, and an example of a simple 2-monad is given by completion under a class of colimits. The notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studied.Comment: 59 page

Hopf measuring comonoids and enrichment

We study the existence of universal measuring comonoids $P(A,B)$ for a pair of monoids $A$, $B$ in a braided monoidal closed category, and the associated enrichment of a category of monoids over the monoidal category of comonoids. In symmetric categories, we show that if $A$ is a bimonoid and $B$ is a commutative monoid, then $P(A,B)$ is a bimonoid; in addition, if $A$ is a cocommutative Hopf monoid then $P(A,B)$ always is Hopf. If $A$ is a Hopf monoid, not necessarily cocommutative, then $P(A,B)$ is Hopf if the fundamental theorem of comodules holds; to prove this we give an alternative description of the dualizable $P(A,B)$-comodules and use the theory of Hopf (co)monads. We explore the examples of universal measuring comonoids in vector spaces and graded spaces.Comment: 30 pages. Version 2: re-arrangement of material; expansion of previous section 6, splitting into current sections 6,7,8; fix of graded algebras example, section 11; appendix removed; other minor fixes and edit

Teaching students about chemical elements using daily-life contexts

Learning the names and symbols for chemical elements is a task that students often find dull, although it is of crucial importance for understanding chemistry. In this respect, the use of games or similar play activities could make the learning experience more enjoyable. This paper presents the results of a study in which two tasks involving play (TIPs) and based on daily-life contexts (football and the home) were used to teach the names and symbols of chemical elements. The experimental group comprised 38 year-10 students who studied this topic through a teaching unit built around the TIPs. A control group of 67 year-10 students followed a traditional teaching approach to the same topic. The effectiveness of the TIPs was assessed using three items, administered pre- and post-test, that explored students’ knowledge about metallic and non-metallic elements and their ability to identify them in their everyday environment. Following the TIP-based teaching unit, students in the experimental group gave a higher percentage of appropriate answers, with the Wilcoxon test indicating significant post-test differences for all three items. However, the Kolgomorov-Smirnov test indicated that the experimental and control groups only differed significantly at post-test in their ability to give the names and symbols of non-metals, with the experimental group performing better. Memorising the names and symbols of chemical elements is a complex task for students, and identifying their presence in everyday environments appears to be particularly difficult. However, the results suggest that the use of TIPs linked to daily-life contexts could help students with their learning of this topic.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Proyecto ‘I+D Excelencia’ EDU2013-41952-

Identification of students' mental models about the milk transformation in yogurt

A review of the scientific literature reveals that there are still few researches on the conceptions of secondary school students about chemical reactions involving microorganisms, especially those related to the mental models that students use in their explanations. This paper describes a study concerning the different mental models related to the milk transformation into yogurt with 83 students from a Spanish secondary school of 8th and 9th grade (13-16 years) developed in the framework of a research that intends to use the elaboration of this product as a context for the teaching and learning of chemical reactions through modeling approaches. In order to identify the mental models of the students, in this paper we consider the milk transformation into yogurt as a process in which its main components are: the entities involved (milk and bacteria), the interaction between them and the result (yogurt). A simplified school model of this process would involve students considering that bacteria use the sugar in milk to transform it into lactic acid through a chemical reaction to obtain the necessary energy. Using this scheme in interaction with the students' answers, the underlying mental models were identified. Although almost half of the students showed great difficulties explaining the process, five models have been identified. Students often consider the milk transformation into yogurt primarily as a physical process of agglutination or change of state. These models are far from a school model of reference in which the bacteria have a fundamental role in the transformation of milk into yogurt by a chemical reaction.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Learning from citizen participation for accountability in Nampula province

The Citizen Engagement Program (CEP) in Mozambique is an empowerment and accountability program aiming to improve the quality of health and education services through supporting citizens to monitor them. The program supports citizens to engage with service providers to address identified problems; it also aims to generate evidence for policy and program improvement at the local and national levels. This case study is structured in three main sections. The first section provides a background to set the context in which organizations such as Facilidade emerged across Mozambique, with reference to the ‘third generation’ of decentralization policies in Sub-Saharan Africa and the growing expectation over nearly two decades of ‘participation’ as a magic bullet to improve service-delivery and governance. As well, this section will give an overview of the methodology, some of the assumptions behind the approach and the challenges and questions that the process raised. The second section presents the findings of the research. These are structured around four themes: practices of participation; citizenship building for accountability; inclusion challenges; and other positive outcomes from the work with citizens. Finally, the third section provides conclusions and spells out questions that remain after this exercise. These questions will be useful for CEP, as well as other social accountability initiatives, to bear in mind when thinking about citizen participation for accountability.UKAIDIrish AidDANID

Autonomous Pseudomonoids

In this dissertation we generalise the basic theory of Hopf algebras to the context of autonomous pseudomonoids in monoidal bicategories. Autonomous pseudomonoids were introduced in [13] as generalisations of both autonomous monoidal categories and Hopf algebras. Much of the theory of autonomous pseudomonoids developed in [13] was inspired by the example of autonomous (pro)monoidal enriched categories. The present thesis aims to further develop the theory with results inspired by Hopf algebra theory instead. We study three important results in Hopf algebra theory: the so-called "fundamental theorem of Hopf modules", the "Drinfel'd quantum double" and its relation with the centre of monoidal categories, and " Radford's formula". The basic result of this work is a general fundamental theorem of Hopf modules that establishes conditions equivalent to the existence of a left dualization. With this result as a base, we are able to construct the centre (defined in [83]) and the lax centre of an autonomous pseudomonoid as an Eilenberg-Moore construction for certain monad. As an application we show that the Drinfel'd double of a finite-dimensional Hopf algebra is equivalent to the centre of the associated pseudomonoid. The next piece of theory we develop is a general Radford's formula for autonomous map pseudomonoids formula in the case of a (coquasi) Hopf algebra. We also introduce "unimodular" autonomous pseudomonoids. In the last part of the dissertation we apply the general theory to enriched categories with a (chosen) class of (co)limits, with emphasis in the case of finite (co)limits. We construct tensor products of such categories by means of pseudo-commutative enriched monads (a slight generalisation of the pseudo-commutative 2-monads of [37], and showing that lax-idempotent 2-monads are pseudo-commutative. Finally we apply the general theory developed for pseudomonoids to deduce the main results of [27].This work was supported by an Internal Graduate Studentship, Trinity College, Cambridge

Frameworks for Urban Conservation: Social Equality Through Housing Tenure in Mexican Historic Cities. Cases of Mexico City and Guadalajara

Since the mid-2000’s Mexico City’s local authorities sought to develop and implement an urban conservation-based Management Plan (2011) for the historic centre, a similar process was pursued for Guadalajara’s historic centre through the Partial Plan (2017). These instruments have aimed to shift from a national monument-centred agenda to follow recent UNESCO instruments that seek to integrate heritage and urban planning with the aim to ensure social and urban equality across existing and prospective residents. But with local authorities’ limited capacity, this shift has resulted in local planning instruments that promote urban renewal and market-based housing development agendas. The aim of this research is to examine the extent to which urban conservation frameworks within planning instruments for historic centres have achieved social equality by ensuring housing tenure security. This research took a cross-sectional two-case study with a predominantly qualitative lens for a mixed-method approach to develop in-depth knowledge of similarities and differences across the cases, which function under national legislation but are driven by local agendas. Based on a Discursive Analysis framework, 46 semi-structured interviews were conducted as primary data sources, focusing on key officers, academics, and residents across both cities. National legislation for heritage conservation, planning and housing as well as local planning instruments were analysed to pin-down key strategies. From this, the practices of dominant discourses to address each historic centre were located within spatial transformation and housing development processes in contexts that have complex social urban dynamics. Following a conscientious qualitative analysis of the collected data, the main findings of this thesis suggest historic centres are repositioned as commodified urban contexts with cultural value where a market-dominant housing agenda is articulated and promoted. This thesis argues that the combination of stagnant heritage conservation policies and deficient institutional capacity has increased a disproportionate private sector reliance. Thus, producing diminished housing tenure opportunities for low-income groups. The effects of this have been experienced at urban and housing levels by existing communities. This leaves room for non-exclusionary urban conservation approaches within planning instruments to ensure more inclusive housing agendas and outcomes