8 research outputs found
The relationship between the diagonal and the bar constructions on a bisimplicial set
AbstractThe aim of this paper is to prove that the homotopy type of any bisimplicial set X is modelled by the simplicial set W¯X, the bar construction on X. We stress the interest of this result by showing two relevant theorems which now become simple instances of it; namely, the Homotopy colimit theorem of Thomason, for diagrams of small categories, and the generalized Eilenberg–Zilber theorem of Dold–Puppe for bisimplicial Abelian groups. Among other applications, we give an algebraic model for the homotopy theory of (not necessarily path-connected) spaces whose homotopy groups vanish in degree 4 and higher
HomotopĂa cilĂndrica generalizada
Desde el punto de vista algebraico, son varios los autores que han estudiado la homotopĂa a travĂ©s de un funtor cilindro. Tomando como modelo la axiomática de Baues [H.J. Baues "Algebraic Homotopy", Cambridge University Pressm 1989], el autor presenta en esta tesis unos axiomas para un funtor cilindro, transformaciones naturales y una familia de cofibraciones, que permiten obtener homotopĂa en categorĂas más generales (I-categorĂas generalizadas), sin necesidad de que los objetos sean cofibrantes y sin necesidad de emplear puntos base para obtener los grupos de homotopĂa. Esta homotopĂa se define relativa a la familia de cofibraciones de la categorĂa, y permite obtener grupos de homotopĂa generalizados, y sucesiones exactas de estos. Se definen acciones de grupos de homotopĂa generalizada, equivariantes sobre las citadas sucesiones. Además, se generaliza a esta categorĂa el concepto de conexidad por caminos de los espacios topolĂłgicos. Se estudia la homotopĂa referida a un objeto fijo de la categorĂa, y se obtiene que los grupos de homotopĂa punteados por dicho objeto y los grupos de homotopĂa de un objeto referidos a otro objeto, son casos particulares de los grupos de homotopĂa generalizada. Se ofrece tambiĂ©n la teorĂa dual, a travĂ©s de un funtor caminos y una familia de fibraciones, y se concluye dando ejemplos concretos de categorĂas que soportan esta estructura generalizada con cilindro
Artisanal trawl fisheries as a sentinel of marine litter pollution
Systematic seafloor surveys are a highly desirable method of marine litter monitoring, but the high costs involved in seafloor sampling are not a trivial handicap. In the present work, we explore the opportunity provided by the artisanal trawling fisheries to obtain systematic data on marine litter in the Gulf of Cadiz between 2019 and 2021. We find that plastic was the most frequent material, with a prevalence of single-use and fishing-related items. Litter densities decreased with increasing distance to shore with a seasonal migration of the main litter hotspots. During pre-lockdown and post-lockdown stages derived from COVID-19, marine litter density decreased by 65 %, likely related to the decline in tourism and outdoor recreational activities. A continuous collaboration of 33 % of the local fleet would imply a removal of hundreds of thousands of items each year. The artisanal trawl fishing sector can play a unique role of monitoring marine litter on the seabe