QEFTCFOHC · Quillen equivalences for the cross-fertilization of higher categories
6РП — Действия „Мария Кюри“
- Период
- 2006-09-01 → 2008-08-31
- Финансиране от ЕС
- 143 433 €
- Участници
- 1
- Схема
- EIF
Линиите свързват координатора с партньорите.
Накратко на български
Високоразмерните категории в математиката се изследват чрез създаване на връзки между различни теории, като например опетопичната и сегаличната. Това помага за обединяване на разрознените знания и улеснява работата в областта на физиката, компютърните науки и логиката.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Цел на проекта
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.
Оригинален текст от CORDIS (на английски).
Участници
- UNIVERSITE DE NICE - SOPHIA ANTIPOLIS · NICEКоординаторФранция
Връзки
Данни: CORDIS, © Европейски съюз