Weighted limits in simplicial homotopy theory

We extend the theory of Quillen adjunctions by combining ideas of homotopical algebra and of enriched category theory. Our results describe how the formulas for homotopy colimits of Bousfield and Kan arise from general formulas describing the derived functor of the weighted colimit functor.

The Euler characteristic of a category

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula is proved for the cardinality of a colimit of sets, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Rota's Möbius inversion from posets to categories.

On two examples by Iyama and Yoshino

In a recent paper Iyama and Yoshino consider two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen-Macaulay modules in terms of linear algebra data. In this paper we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second approach we use Orlov's result on the graded singularity category. We obtain some new results on the singularity category of isolated singularities which may be interesting in their own right.

Aproximació a les conceptualitzacions gramaticals d’alumnes de secundària a propòsit de les classes de mots

El treball vol aprofundir en les conceptualitzacions gramaticals dels alumnes de secundària, particularment en els sabers que mobilitzen quan han de determinar la classe lèxica de certes paraules (els mots analitzats pertanyen a categories “simples” com les de nom, verb, adjectiu i adverbi). Per a tal fi s’han enquestat 141 alumnes i se n’han entrevistat 18 (es tracta d’estudiants de tots els nivells de secundària d’un mateix institut). L’estudi posa en evidència la diversitat de procediments i de conceptualitzacions mobilitzats, progressivament complexos a mesura que avança l’escolarització, però també la freqüent manca de coherència entre els procediments aplicats –sovint mecànics– i els conceptes que afloren –sovint purament memorístics– en el discurs metalingüístic d’aquests estudiants.

Does urban sprawl increase the costs of providing local public services? Evidence from Spanish municipalities

This paper examines the impact of urban sprawl, a phenomenon of particular interest in Spain, which is currently experiencing this process of rapid, low-density urban expansion. Many adverse consequences are attributed to urban sprawl (e.g., traffic congestion, air pollution and social segregation), though here we are concerned primarily with the rising costs of providing local public services. Our initial aim is to develop an accurate measure of urban sprawl so that we might empirically test its impact on municipal budgets. Then, we undertake an empirical analysis using a cross-sectional data set of 2,500 Spanish municipalities for the year 2003 and a piecewise linear function to account for the potentially nonlinear relationship between sprawl and local costs. The estimations derived from the expenditure equations for both aggregate and six disaggregated spending categories indicate that low-density development patterns lead to greater provision costs of local public services.

Localization of algebras over coloured operads

We give sufficient conditions for homotopical localization functors to preserve algebras over coloured operads in monoidal model categories. Our approach encompasses a number of previous results about preservation of structures under localizations, such as loop spaces or infinite loop spaces, and provides new results of the same kind. For instance, under suitable assumptions, homotopical localizations preserve ring spectra (in the strict sense, not only up to homotopy), modules over ring spectra, and algebras over commutative ring spectra, as well as ring maps, module maps, and algebra maps. It is principally the treatment of module spectra and their maps that led us to the use of coloured operads (also called enriched multicategories) in this context.

Note on a theorem of Bousfield and Friedlander

We examine the proof of a classical localization theorem of Bousfield and Friedlander and we remove the assumption that the underlying model category be right proper. The key to the argument is a lemma about factoring in morphisms in the arrow category of a model category.

A model category structure on the category of simplicial multicategories

We establish a Quillen model structure on simplicial(symmetric) multicategories. It extends the model structure on simplicial categories due to J. Bergner [2]. We observe that our technique of proof enables us to prove a similar result for (symmetric) multicategories enriched over other monoidal model categories than simplicial sets. Examples include small categories, simplicial abelian groups and compactly generated Hausdorff spaces.

Polynomial functors and trees

We explore the relationship between polynomial functors and trees. In the first part we characterise trees as certain polynomial functors and obtain a completely formal but at the same time conceptual and explicit construction of two categories of rooted trees, whose main properties we describe in terms of some factorisation systems. The second category is the category Ω of Moerdijk and Weiss. Although the constructions are motivated and explained in terms of polynomial functors, they all amount to elementary manipulations with finite sets. Included in Part 1 is also an explicit construction of the free monad on a polynomial endofunctor, given in terms of trees. In the second part we describe polynomial endofunctors and monads as structures built from trees, characterising the images of several nerve functors from polynomial endofunctors and monads into presheaves on categories of trees. Polynomial endofunctors and monads over a base are characterised by a sheaf condition on categories of decorated trees. In the absolute case, one further condition is needed, a projectivity condition, which serves also to characterise polynomial endofunctors and monads among (coloured) collections and operads.

On an extension of the notion of Reedy category

"Vegeu el resum a l'inici del document del fitxer adjunt."

On the trace of an endofunctor of a small category

The trace of a square matrix can be defined by a universal property which, appropriately generalized yields the concept of "trace of an endofunctor of a small category". We review the basic definitions of this general concept and give a new construction, the "pretrace category", which allows us to obtain the trace of an endofunctor of a small category as the set of connected components of its pretrace. We show that this pretrace construction determines a finite-product preserving endofunctor of the category of small categories, and we deduce from this that the trace inherits any finite-product algebraic structure that the original category may have. We apply our results to several examples from Representation Theory obtaining a new (indirect) proof of the fact that two finite dimensional linear representations of a finite group are isomorphic if and only if they have the same character.

Un estudi de les argumentacions d’estudiants anglesos i catalans en activitats de resolució de problemes no formals en ciències i de les estratègies didàctiques dels professors que afavoreixen l’argumentació a les classes

Una de les contribucions de la recerca sobre concepcions prèvies dels estudiants en ciències durant els darrers 25 anys ha estat mostrar la influència del context sociocultural dels nois i noies en les idees i concepcions que desenvolupen i mantenen des de la seva infància. Hi ha l’acord que algunes diferències en les concepcions poden dependre de la cultura social en la qual s’integren. Alguns investigadors també pensen que els esquemes argumentatius també poden ser influenciats per la cultura de les comunitats. Els contextos Català i Anglès semblen similars, ambdós formen part del context cultural de les societats desenvolupades; per tant, podem pensar que els esquemes argumentatius que els estudiants apliquen, poden tenir moltes similituds, però també importants diferències. Les dades analitzades provenen de les respostes escrites dels estudiants individuals i de les transcripcions de 8 grups de discussió sobre quatre tasques. L’anàlisi es fa a tres nivells: 1)comparació del nombre d’arguments entre tasques i entre països, 2) qualitativa i descriptiva comparació entre tipus d’esquemes argumentatius per tasques i per països i 3) explicació de tipus d’esquemes argumentatius que es donen molt, i identificació d’estructures argumentatives complexes que lliguen diversos esquemes en un argument més gran i que poden caracteritzar l’argumentació d’alguns grups (aplicant Toulmin) i que poden ser indicadors d’aspectes cooperatius i de canvis de punts de vista en les discussions. Els resultants ens indiquen que encara que els estudiants Catalans dediquen més temps a les discussions, la ratio nombre d’esquemes per unitat de temps és similar als dos països. S’han trobar algunes diferències entre tipus d'esquemes per països i per tasques, també que molts arguments es basen en valors i idees preconcebudes. S’han pogut identificar també algunes estructures argumentatives complexes no gaire comunes.

A multi-purpose grammar generating a multi-scale integrated analysis of Laos

In this study we propose an application of the MuSIASEM approach which is used to provide an integrated analysis of Laos across different scales. With the term “integrated analysis across scales” we mean the generation of a series of packages of quantitative indicators, characterizing the performance of the socioeconomic activities performed in Laos when considering: (i) different hierarchical levels of organization (farming systems described at the level of household, rural villages, regions of Laos, the whole country level); and (ii) different dimensions of analysis (economic dimension, social dimension, ecological dimension, technical dimension). What is relevant in this application is that the information carried out by these different packages of indicators is integrated in a system of accounting which establishes interlinkages across these indicators. This is a essential feature to study sustainability trade-offs and to build more robust scenarios of possible changes. The multi-scale integrated representation presented in this study is based on secondary data (gathered in a three year EU project – SEAtrans and integrated by other available statistical sources) and it is integrated in GIS, when dealing with the spatial representation of Laos. However, even if we use data referring to Laos, the goal of this study is not that of providing useful information about a practical policy issue of Laos, but rather, to illustrate the possibility of using a multipurpose grammar to produce an integrated set of sustainability indicators at three different levels: (i) local; (ii) meso; (iii) macro level. The technical issue addressed is the simultaneous adoption of two multi-level matrices – one referring to a characterization of human activity over a set of different categories, and another referring to a characterization of land uses over the same set of categories. In this way, it becomes possible to explain the characteristics of Laos (an integrated set of indicators defining the performance of the whole country) in relation to the characteristics of the rural Laos and urban Laos. The characteristics of rural Laos, can be explained using the characteristics of three regions defined within Laos (Northern Laos, Central Laos and Southern Laos), which in turn can be defined (using an analogous package of indicators), starting from the characteristics of three main typologies of farming systems found in the regions.

Applications of the MuSIASEM approach to study changes in the metabolic pattern of Catalonia

This document presents an integrated analysis of the performance of Catalonia based on an analysis of how the energy consumption (measured at the societal level for the Catalan Society) is used within both the productive sectors of the economy and the household, to generate added value, jobs, and to guarantee a given level of material standard of living to the population. The trends found in Catalonia are compared to the trends of other European Countries to contextualize the performance of Catalonia with respect to other societies that have followed different paths of economic development. The first part of the document consists of the Multi-Scale Integrated Analysis of Societal and Ecosystem Metabolism (MuSIASEM) approach that has been used to provide this integrated analysis of Catalan Society across different scales (starting from an analysis of the specific sectors of the Catalan economy as an Autonomous Community and scaling up to an intra-regional (European Union 14) comparison) and across different dimensions of analyses of energy consumption coupled with added value generation. Within the scope of this study, we observe the various trajectories of changes in the metabolic pattern for Catalonia and the EU14 countries in the Paid Work Sectors composed of namely, the Agricultural Sector, the Productive Sector and the Services and Government Sector also in comparison with the changes in the household sector. The flow intensities of the exosomatic energy and the added value generated for each specific sector are defined per hour of human activity, thus characterized as exosomatic energy (MJ/hour) (or Exosomatic Metabolic Rate) and added value (€/hour) (Economic Labour Productivity) across multiple levels. Within the second part of the document, the possible usage of the MuSIASEM approach to land use analyses (using a multi-level matrix of categories of land use) has been conducted.

Authoritarian Responses to Foreign Pressure: Spending, Repression, and Sanctions

This paper explores how international sanctions affect authoritarian rulers’ decisions concerning repression and public spending composition, and how different authoritarian rulers respond to foreign pressure. If sanctions are assumed to increase the price of loyalty to the regime, then rulers whose budgets are not severely constrained by sanctions will tend to increase spending in those categories that most benefit their core support groups. In contrast, when constraints are severe due to reduced aid and trade, dictators are expected to greatly increase their levels of repression. Using data on regime types, public expenditures and spending composition (1970–2000) as well as on repression levels (1976–2001), we show that the empirical patterns conform well to our theoretical expectations. Single-party regimes, when targeted by sanctions, increase spending on subsidies and transfers which largely benefit more substantial sectors of the population and especially the urban classes. Likewise, military regimes increase their expenditures on goods and services, which include military equipment and soldiers’ and officers’ wages. Conversely, personalist regimes reduce spending in all categories, especially capital expenditures, while increasing repression much more than other regime types when targeted by sanctions.