Objectif Higher-dimensional categories have developed rapidly in the last few years but the theory is still rather disjointed. To date, little work has been completed to compare and link up the different parts of the theory. The applicant's PhD thesis contains the first full comparison theorems in the subject. Such a higher-dimensional language and a body of relevant results is already found in a rudimentary way throughout algebraic topology, and a need for such has arisen, almost simultaneously, in areas of mathematical physics, algebraic geometry, computer science, and logic. In all these fields, higher-dimensional structures exist, and we need a coherent way of studying them.The aim of this project is to construct Quillen equivalences between different theories to enable cross-fertilization of them. Different theories have been proposed with different emphases, and developed and understood to differing degrees. By linking the theories, we will be able to use the developments in one theory to help us in another; this cross-fertilization will enable a more coherent overall framework for higher-dimensional categories. Model categories are the organisational principle of a 'good' homotopy theory; one often considers that to define a good homotopy theory is just to construct a model category. Then Quillen equivalence is a special kind of adjunction between model categories.This notion is subtler than ordinary equivalence of categories and was coined as the right notion of equivalence up to homotopy for model categories. This sophisticated and well-developed theory seems to be the mandatory tool for formalizing the comparisons proposed in this project. The proposal concentrates on comparing the Opetopic and Segalic theories, drawing on the expertise of the applicant and the host institution respectively. The applicant's move to the Laboratoire Dieudonne will thus enable a cross-fertilization of competencies as well as of higher-categorical theories. Champ scientifique natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencescomputer and information sciencesnatural sciencesmathematicspure mathematicstopologyalgebraic topologynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Mots‑clés Higher-dimensional category theory Quillen equivalence Quillen model category theory Segal categories comparison of foundations simplicial homotopy theory Programme(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Thème(s) MOBILITY-2.1 - Marie Curie Intra-European Fellowships (EIF) Appel à propositions FP6-2002-MOBILITY-5 Voir d’autres projets de cet appel Régime de financement EIF - Marie Curie actions-Intra-European Fellowships Coordinateur UNIVERSITE DE NICE SOPHIA-ANTIPOLIS Contribution de l’UE Aucune donnée Adresse 28 avenue de Valrose-Parc Valrose NICE France Voir sur la carte Liens Site web Opens in new window Coût total Aucune donnée
