Alguns punts d'àlgebra homotopica

L'any 1967, D. Quillen introduí la noció de categoria de models, estructura adaptada a l'estudi de l'àlgebra homotòpica. Una estructura de categoria de models en una categoria donada consisteix en l'elecció de tres classes de morfismes distingits, sotmeses a uns certs axiomes, que permeten definir una teoria d'homotopia en la categoria i representacions concretes de la categoria homotòpica. Així mateix, una estructura de categoria de models dóna criteris per a l'existència i el càlcul dels functors derivats de functors definits entre categories que posseixen la dita estructura. Aquest és el context de la memòria. Pel que fa a les categories de models, s'hi demostra que categories habituals de l'àlgebra homològica diferencial i de l'homotopia racional, com són la de mòduls dg a coeficients en una àlgebra dgc, o la d'extensions d'una àlgebra dgc fixada, tenen una tal estructura. Com a aplicació, es demostra l'existència dels functors derivats dels functors "producte tensorial" i "indescomponibles" (cap. II). Un tipus de models particulars són els models minimals, introduïts a l'homotopia racional per Sullivan. En la memòria es proposa una definició categòrica dels mateixos, que comprèn altres models "minimals" de la literatura (resolucions minimals de Tate-Jozefiak, per exemple). Així mateix es demostra l'existència de tals models en les categories de complexos de cocadenes a coeficients en un anell local i en la de mòduls dg a coeficients en una àlgebra dgc (cap. IV). El punt central de la memòria és l'estudi de les estructures de categories de models i dels models minimals en les categories bifi-brades, la definició de les quals és deguda a Grothendieck. Una categoria bifibrada pot pensar-se com una família de categories parame-tritzada per una altra categoria. Així, per exemple, les categories de mòduls dg a coeficients en una àlgebra dgc qualsevol o la categoria de morfismes d'àlgebres dgc són categories bifibrades. En la memòria es demostra que tals categories admeten una estructura natural de categoria de models i es caracteritzen els seus models minimals (cap. III i IV). Entre els diversos tipus d'homotopia racional, Sullivan distingeix els formals, com aquells determinats completament per l'àlgebra de cohomologia. Aquesta noció prové d'una obstrucció homotòpica a l'existència d'estructures kälherianes sobre una varietat. En la memòria, es dóna una definició categòrica de formalitat. Aplicada a les categories bifibrades anteriors, permet generalitzar el resultat de Sullivan: la formalitat dels morfismes d'àlgebres dgc és independent del cos base (cap. IV, teorema V). L'últim capítol està dedicat al tor diferencial, functor derivat del producte tensorial de mòduls dg i àlgebres dgc. Els principals resultats són la comparació de les diferents defincions del tor diferencial i la compatibilitat amb els functors d'oblit i dels indescomponibles (cap. V).On 1967 D. Quillen introduced the notion of model category, a structure adapted for the study of homotopical algebra. A model category structure in a given category consists in the election of three types of distinguished morphisms, subject to certain axioms, which allow to define an homotopy theory in the category and specific representations of the homotopy category. Also, a structure of model category provides with criteria for the existence and calculation of derived functors of functors defined among categories which share the above mentioned structure. This is the context to this report. Regarding the model categories, we prove here that, usual categories in diferential homological algebra and in rational homotopy, such as the category of dg-modules over a dgc-algebra, or the category of extensions of a fixed dgc-algebra have such a structure. As an application, we prove the existence of the derived functors of «tensorial product» and «indecomposables» (chapter II). A particular type of models are minimal models, introduced in rational homotopyby Sullivan. In this report we suggest a categorical definition of these models, which includes other minimal models already written about (as, for example Tate-Jozefiakminimal resolutions). Also, we prove the existence of these models in the category of cochain complexes over a local ring and in the category of dg-modules over adgc-algebra. The central theme in this report is the study of the structures of model categories and of minimal models in bifibred categories. We owe the definition of these to Grothendieck. We can consider a bifibred category as a family of categories parametrized by another category. For example, the category of dg-modules over anydgc-algebra or the category of morphisms of dgc-algebras are bifibred categories. In the report we prove that such categories admit a natural structure of model category and we characterize their minimal models (chapters III and IV). Among the diferent types of rational homotopy , Sullivan points out the formals as the ones being determinated entirely by the cohomology algebra. This notion derives from the existence of an homotopic obstruction to the existence of k¨alherianstructures on a variety. In this report we give a categorical definition of formality. This definition, applied to the above mentioned bifibred categories, allows a generalization of the results of Sullivan: formality of dgc-algebra morphisms does not depend on theground field (chapter IV, theoreme V). The last chapter centres on the diferential tor, the derived functor of tensorial product of dg-modules and dgc-algebras. The main results are the comparison between the diferent definitions of this diferential tor and the compatibility with the forgetful functor and the indecomposable functor (chapter V)

Passive smoking at home is a risk factor for community-acquired pneumonia in older adults: a population-based case-control study

OBJECTIVE: To assess whether passive smoking exposure at home is a risk factor for community-acquired pneumonia (CAP) in adults. SETTING: A population-based case-control study was designed in a Mediterranean area with 860 000 inhabitants >14 years of age. PARTICIPANTS: 1003 participants who had never smoked were recruited. PRIMARY AND SECONDARY OUTCOME MEASURES: Risk factors for CAP, including home exposure to passive smoking, were registered. All new cases of CAP in a well-defined population were consecutively recruited during a 12-month period. METHODS: A population-based case-control study was designed to assess risk factors for CAP, including home exposure to passive smoking. All new cases of CAP in a well-defined population were consecutively recruited during a 12-month period. The subgroup of never smokers was selected for the present analysis. RESULTS: The study sample included 471 patients with CAP and 532 controls who had never smoked. The annual incidence of CAP was estimated to be 1.14 cases×10(-3) inhabitants in passive smokers and 0.90×10(-3) in non-passive smokers (risk ratio (RR) 1.26; 95% CI 1.02 to 1.55) in the whole sample. In participants ≥65 years of age, this incidence was 2.50×10(-3) in passive smokers and 1.69×10(-3) in non-passive smokers (RR 1.48, 95% CI 1.08 to 2.03). In this last age group, the percentage of passive smokers in cases and controls was 26% and 18.1%, respectively (p=0.039), with a crude OR of 1.59 (95% CI 1.02 to 2.38) and an adjusted (by age and sex) OR of 1.56 (95% CI 1.00 to 2.45). CONCLUSIONS: Passive smoking at home is a risk factor for CAP in older adults (65 years or more)

Relationship between the use of inhaled steroids for chronic respiratory diseases and early outcomes in community-acquired pneumonia.

Background The role of inhaled steroids in patients with chronic respiratory diseases is a matter of debate due to the potential effect on the development and prognosis of community-acquired pneumonia (CAP). We assessed whether treatment with inhaled steroids in patients with chronic bronchitis, COPD or asthma and CAP may affect early outcome of the acute pneumonic episode. Methods Over 1-year period, all population-based cases of CAP in patients with chronic bronchitis, COPD or asthma were registered. Use of inhaled steroids were registered and patients were followed up to 30 days after diagnosis to assess severity of CAP and clinical course (hospital admission, ICU admission and mortality). Results Of 473 patients who fulfilled the selection criteria, inhaled steroids were regularly used by 109 (23%). In the overall sample, inhaled steroids were associated with a higher risk of hospitalization (OR=1.96, p = 0.002) in the bivariate analysis, but this effect disappeared after adjusting by other severity-related factors (adjusted OR=1.08, p=0.787). This effect on hospitalization also disappeared when considering only patients with asthma (OR=1.38, p=0.542), with COPD alone (OR=4.68, p=0.194), but a protective effect was observed in CB patients (OR=0.15, p=0.027). Inhaled steroids showed no association with ICU admission, days to clinical recovery and mortality in the overall sample and in any disease subgroup. Conclusions Treatment with inhaled steroids is not a prognostic factor in COPD and asthmatic patients with CAP, but could prevent hospitalization for CAP in patients with clinical criteria of chronic bronchitis

Alguns punts d'àlgebra homotòpica

L'any 1967, D. Quillen introduí la noció de categoria de models, estructura adaptada a l'estudi de l'àlgebra homotòpica. Una estruc¬tura de categoria de models en una categoria donada consisteix en l'elecció de tres classes de morfismes distingits, sotmeses a uns certs axiomes, que permeten definir una teoria d'homotopia en la categoria i representacions concretes de la categoria homotòpica. Així mateix, una estructura de categoria de models dóna criteris per a l'existència i el càlcul dels functors derivats de functors definits entre categories que posseixen la dita estructura. Aquest és el context de la memòria.Pel que fa a les categories de models, s'hi demostra que cate¬gories habituals de l'àlgebra homològica diferencial i de l'homotopia racional, com són la de mòduls dg a coeficients en una àlgebra dgc, o la d'extensions d'una àlgebra dgc fixada, tenen una tal estructura. Com a aplicació, es demostra l'existència dels functors derivats dels functors "producte tensorial" i "indescomponibles" (cap. II).Un tipus de models particulars són els models minimals, in¬troduïts a l'homotopia racional per Sullivan. En la memòria es proposa una definició categòrica dels mateixos, que comprèn altres models "minimals" de la literatura (resolucions minimals de Tate-Jozefiak, per exemple). Així mateix es demostra l'existència de tals models en les categories de complexos de cocadenes a coeficients en un anell local i en la de mòduls dg a coeficients en una àlgebra dgc (cap. IV).El punt central de la memòria és l'estudi de les estructures de categories de models i dels models minimals en les categories bifi-brades, la definició de les quals és deguda a Grothendieck. Una cate¬goria bifibrada pot pensar-se com una família de categories parame-tritzada per una altra categoria. Així, per exemple, les categories de mòduls dg a coeficients en una àlgebra dgc qualsevol o la categoria de morfismes d'àlgebres dgc són categories bifibrades. En la memòria es demostra que tals categories admeten una estructura natural de categoria de models i es caracteritzen els seus models minimals (cap. III i IV).Entre els diversos tipus d'homotopia racional, Sullivan distingeix els formals, com aquells determinats completament per l'àlgebra de cohomologia. Aquesta noció prové d'una obstrucció homotòpica a l'existència d'estructures kälherianes sobre una varietat. En la memòria, es dóna una definició categòrica de formalitat. Aplicada a les categories bifibrades anteriors, permet generalitzar el resultat de Sullivan: la formalitat dels morfismes d'àlgebres dgc és independent del cos base (cap. IV, teorema V).L'últim capítol està dedicat al tor diferencial, functor derivat del producte tensorial de mòduls dg i àlgebres dgc. Els principals resul¬tats són la comparació de les diferents defincions del tor diferencial i la compatibilitat amb els functors d'oblit i dels indescomponibles (cap. V).On 1967 D. Quillen introduced the notion of model category, a structure adapted for the study of homotopical algebra. A model category structure in a given category consists in the election of three types of distinguished morphisms, subject to certain axioms, which allow to define an homotopy theory in the category and specific representations of the homotopy category. Also, a structure of model category provides with criteria for the existence and calculation of derived functors of functors defined among categories which share the above mentioned structure. This is the context to this report.Regarding the model categories, we prove here that, usual categories in diferential homological algebra and in rational homotopy, such as the category of dg-modules over a dgc-algebra, or the category of extensions of a fixed dgc-algebra have such a structure. As an application, we prove the existence of the derived functors of "tensorial product" and "indecomposables" (chapter II).A particular type of models are minimal models, introduced in rational homotopyby Sullivan. In this report we suggest a categorical definition of these models, which includes other minimal models already written about (as, for example Tate-Jozefiakminimal resolutions). Also, we prove the existence of these models in the category of cochain complexes over a local ring and in the category of dg-modules over adgc-algebra.The central theme in this report is the study of the structures of model categories and of minimal models in bifibred categories. We owe the definition of these to Grothendieck. We can consider a bifibred category as a family of categories parametrized by another category. For example, the category of dg-modules over anydgc-algebra or the category of morphisms of dgc-algebras are bifibred categories. In the report we prove that such categories admit a natural structure of model category and we characterize their minimal models (chapters III and IV).Among the diferent types of rational homotopy , Sullivan points out the formals as the ones being determinated entirely by the cohomology algebra. This notion derives from the existence of an homotopic obstruction to the existence of k¨alherianstructures on a variety. In this report we give a categorical definition of formality. This definition, applied to the above mentioned bifibred categories, allows a generalization of the results of Sullivan: formality of dgc-algebra morphisms does not depend on theground field (chapter IV, theoreme V).The last chapter centres on the diferential tor, the derived functor of tensorial product of dg-modules and dgc-algebras. The main results are the comparison between the diferent definitions of this diferential tor and the compatibility with the forgetful functor and the indecomposable functor (chapter V)

Moduli spaces and formal operads

Let overline{M}_{g,n} be the moduli space of stable algebraic curves of genus g with n marked points. With the operations which relate the different moduli spaces identifying marked points, the family (overline{M}_{g,n})_{g,n} is a modular operad of projective smooth Deligne-Mumford stacks, overline{M}. In this paper we prove that the modular operad of singular chains C_*(overline{M};Q) is formal; so it is weakly equivalent to the modular operad of its homology H_*(overline{M};Q). As a consequence, the "up to homotopy" algebras of these two operads are the same. To obtain this result we prove a formality theorem for operads analogous to Deligne-Griffiths-Morgan-Sullivan formality theorem, the existence of minimal models of modular operads, and a characterization of formality for operads which shows that formality is independent of the ground field

A Cartan-Eilenberg approach to Homotopical Algebra

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences such that there is an equivalence of categories between its localisation with respect to weak equivalences and the relative localisation of the subcategory of cofibrant objects with respect to strong equivalences. This equivalence of categories allows us to extend the classical theory of derived additive functors to this non additive setting. The main examples include Quillen model categories and categories of functors defined on a category endowed with a cotriple (comonad) and taking values on a category of complexes of an abelian category. In the latter case there are examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications of our theory, we establish a very general acyclic models theorem

Monoidal functors, acyclic models and chain operads

We prove that for a topological operad $P$ the operad of oriented cubical singular chains, C^{\ord}_\ast(P), and the operad of simplicial singular chains, $S_\ast(P)$, are weakly equivalent. As a consequence, C^{\ord}_\ast(P\nsemi\mathbb{Q}) is formal if and only if S_\ast(P\nsemi\mathbb{Q}) is formal, thus linking together some formality results which are spread out in the literature. The proof is based on an acyclic models theorem for monoidal functors. We give different variants of the acyclic models theorem and apply the contravariant case to study the cohomology theories for simplicial sets defined by $R$-simplicial differential graded algebras