Objective
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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics applied mathematics mathematical physics
- natural sciences computer and information sciences
- natural sciences mathematics pure mathematics topology algebraic topology
- natural sciences mathematics pure mathematics geometry
- natural sciences mathematics pure mathematics algebra algebraic geometry
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2002-MOBILITY-5
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
NICE
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.