Cohomologia de grupoides ordenados

“Una de las ideas que persiguen las distintas homotopías abstractas es dar una axiomática en categorías generales de forma que se obtengan categorías homotopicas en el sentido de J. H. C. Whithead con la axiomática clásica para espacios topológicos, donde partiendo de dicha categoría se establece una relación de equivalencia (relación de homotopáa) entre los morfismos (aplicaciones continuas) compatible con su composición, de forma que se pueda crear la categoría cociente (categoría de homotopia) en el sentido descrito por S. MacLane en [12]. De esta forma se obtiene una clasificacion de los objetos de la categoría (equivalencia de homotopías). Philip Higgins es un pionero de la idea de usar grupoides en topología, y de interpretar ideas de teoría de grupoides en términos topológicos. Una explicación de su trabajo se encuentra en su libro [6]. El enfoque de Higgins fue desarrollado por Ronnie Brown en [4], en varias direcciones. En [20] se introduce la noción de homotopía para grupoides ordenados y se muestra que la teoría de homotopía abstracta puede ser usada para definir una noción conveniente de equivalencia homotópica de grupoides ordenados ´ y por tanto de semigrupos inversos.

Documenting the Recovery of Vascular Services in European Centres Following the Initial COVID-19 Pandemic Peak: Results from a Multicentre Collaborative Study

Objective: To document the recovery of vascular services in Europe following the first COVID-19 pandemic peak. Methods: An online structured vascular service survey with repeated data entry between 23 March and 9 August 2020 was carried out. Unit level data were collected using repeated questionnaires addressing modifications to vascular services during the first peak (March - May 2020, "period 1"), and then again between May and June ("period 2") and June and July 2020 ("period 3"). The duration of each period was similar. From 2 June, as reductions in cases began to be reported, centres were first asked if they were in a region still affected by rising cases, or if they had passed the peak of the first wave. These centres were asked additional questions about adaptations made to their standard pathways to permit elective surgery to resume. Results: The impact of the pandemic continued to be felt well after countries' first peak was thought to have passed in 2020. Aneurysm screening had not returned to normal in 21.7% of centres. Carotid surgery was still offered on a case by case basis in 33.8% of centres, and only 52.9% of centres had returned to their normal aneurysm threshold for surgery. Half of centres (49.4%) believed their management of lower limb ischaemia continued to be negatively affected by the pandemic. Reduced operating theatre capacity continued in 45.5% of centres. Twenty per cent of responding centres documented a backlog of at least 20 aortic repairs. At least one negative swab and 14 days of isolation were the most common strategies used for permitting safe elective surgery to recommence. Conclusion: Centres reported a broad return of services approaching pre-pandemic "normal" by July 2020. Many introduced protocols to manage peri-operative COVID-19 risk. Backlogs in cases were reported for all major vascular surgeries