Rewriting in higher dimensional linear categories and application to the affine oriented Brauer category

In this paper, we introduce a rewriting theory of linear monoidal categories. Those categories are a particular case of what we will define as linear (n, p)-categories. We will also define linear (n, p)-polygraphs, a linear adapation of n-polygraphs, to present linear (n -- 1, p)-categories. We focus then on linear (3, 2)-polygraphs to give presentations of linear monoidal categories. We finally give an application of this theory in linear (3, 2)-polygraphs to prove a basis theorem on the category AOB with a new method using a rewriting property defined by van Ostroom: decreasingness

Rewriting in the category of Bott-Samelson bimodules

International audienceThe category of Bott-Samelson bimodules is a category studied in representation theory introduced by Soergel. Elias and Williamson introduce a diagrammatic language to present it by generators and relations. Our objective is to compute by rewriting methods relations between relations. For this, we introduce in this work (3,2)-linear polygraphs to take the structure of this category, which is monoidal with a vector space structure on its morphism spaces into account. New difficulties arise from this object. Termination is harder to prove and local confluence has a more restrictive criterion

Coherence of quasi-terminating decreasing 2-polygraphs

International audienceCraig Squier introduced a combinatorial method based on rewriting in order to describe relations amongst relations for presentations of monoids. From a rewriting system he constructed a 2-dimensional combinatorial complex whose 2-cells are generated by relations induced by the rewriting rules. When the rewriting system is confluent and terminating, he characterized the homotopy of this complex in term of confluence diagrams induced by the critical branchings. In this work, we weaken the termination hypothesis and we prove such a result for quasi-terminating decreasing rewriting systems

Coherence of string rewriting systems by decreasingness

Squier introduced a homotopical method in order to describe all the relations amongst rewriting reductions of a confluent and terminating string rewriting system. From a string rewriting system he constructed a 2-dimensional combinatorial complex whose 2-cells are generated by relations induced by the rewriting rules. When the rewriting system is confluent and terminating, the homotopy of this complex can be characterized in term of confluence diagrams induced by the critical branchings of the rewriting system. Such a construction is now used to solve coherence problems for monoids using confluent and terminating string rewriting systems. In this article, we show how to weaken the termination hypothesis in the description of all the relations amongst rewriting reductions. Our construction uses the decreasingness method introduced by van Oostrom. We introduce the notion of decreasing two-dimensional polygraph and we give sufficient conditions for a decreasing polygraph to be extended in a coherent way. In particular, we show how a confluent and quasi-terminating polygraph can be extended into a coherent presentation

Alain Roussillon. Mémoire d’Égypte

Ce numéro d’Égypte/Monde arabe a été lancé en 2017. Il souhaite rendre hommage à Alain Roussillon, disparu prématurément en 2007 à l’âge de 55 ans, alors qu’il dirigeait le CEDEJ. Il réunit les contributions des collègues de sa génération, de ceux qu’il a aidés à s’engager dans des recherches en sciences sociales sur l’Égypte, le Maghreb ou le monde arabe ou d’autres, plus jeunes, qui l’ont lu et pour qui il a été une source d’inspiration. En parallèle à la réédition de certains de ses articles, assurée par Hamit Bozarslan et Laure Guirguis à CNRS Éditions, il s’agit dans ce numéro de réfléchir à son héritage intellectuel : à la postérité des concepts qu’il a forgés, notamment celui de réforme sociale ; aux différents terrains qu’il a explorés, des migrations interarabes aux recompositions des diasporas arabes en Amérique latine ; à la validité des grilles de lecture proposées et à leur pertinence dans l’Égypte d’aujourd’hui. This special issue of Égypte/Monde arabe is a tribute to Alain Roussillon, who passed away prematurely in 2007 at age fifty-five, when he was the director of the CEDEJ. This issue was set in motion in 2017, on the ten-year anniversary of his death. It is an homage from his colleagues, many of whom he helped find a voice in the social sciences research sphere on Egypt and the Arab world. The collection also includes contributions from younger authors who were inspired by his work. To complement this tribute, the editions of the French National Centre for Scientific Research (CNRS) has re-released some of his articles under the supervision of Hamit Bozarslan and Laure Guirguis. The edition reflects on his intellectual legacy and carefully considers the longevity of his concepts. From his work on inter-Arab migrations to the reconfiguration of the Arab diaspora in Latin America, it is timely to re-examine these readings and their relevance in the context of current Egypt

L’Égypte en débats

De quoi parle-t-on, en Égypte, et en quels termes ? Quelles questions et quels problèmes y sont-ils susceptibles de faire l’objet de débats et avec quels enjeux ? Qui prend part à ces débats et dans le cadre de quelles stratégies ? Comment un débat commence-t-il et pourquoi s’arrête-t-il> ? Telles sont les questions auxquelles les contributeurs à la présente livraison d’EMAs’efforcent modestement de répondre. Il ne s’agit pas tant de donner accès au grand mystère de « l’opinion publique » égyptienne et de ses orientations que de montrer comment s’articule un discours social, celui, contrasté, qu’une société tient sur elle-même, pour ainsi dire au jour le jour, en des lieux autorisés, et par la voix d’ayants droit à la parole publique. […

Switch to fulvestrant and palbociclib versus no switch in advanced breast cancer with rising ESR1 mutation during aromatase inhibitor and palbociclib therapy (PADA-1): a randomised, open-label, multicentre, phase 3 trial

International audienc