Objective We will study in this project exciting new interactions and applications between two fundamental modern research areas of mathematics, homotopy theory and higher category theory. These areas of mathematics are used in applied sciences. For instance, homotopy theory is used in robotics and in computer science. Higher category theory studies the way in which complex structures arising for instance in physics, computer science, biology, can be described by a common language, the one of ‘weak n-categories’. In this project, we apply ideas and techniques from homotopy theory to higher category theory. This will provide new and groundbreaking insights into the latter and will return homotopical applications. We will study certain structures which resembles simple algebraic ones but which are in fact much more complex because the defining data are specified ‘up to homotopy’. These structures are called homotopy algebras. We will then study ways in which a homotoy algebra can be made suitably equivalent to a simpler structure, a strict algebra. This process is called rigidification. We will then apply this theory to weak n-categories. We will view one of the models of weak n-categories, due to Tamsamani, as homotopy algebras, and study its rigidification. This will produce a new important type of higher categorical structure, called weakly globular n-fold categories. These will then be used in applications. We will obtain a new way to describe the building blocks of topological spaces, called n-types, and we will understand their connection with iterated loop spaces. We will also pursue other homotopical applications which will lead to the computation of important invariants used to describe topological spaces. Fields of science natural sciencesmathematicspure mathematicsalgebranatural sciencescomputer and information sciencesengineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringrobotics Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) FP7-PEOPLE-2009-RG - Marie Curie Action: "Reintegration Grants" Call for proposal FP7-PEOPLE-2009-RG See other projects for this call Funding Scheme MC-IRG - International Re-integration Grants (IRG) Coordinator UNIVERSITY OF LEICESTER EU contribution € 100 000,00 Address UNIVERSITY ROAD LE1 7RH Leicester United Kingdom See on map Region East Midlands (England) Leicestershire, Rutland and Northamptonshire Leicester Activity type Higher or Secondary Education Establishments Administrative Contact Marie Adams (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Participants (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all Masarykova univerzita Participation ended Czechia EU contribution No data Address Zerotinovo namesti 9 601 77 Brno See on map Region Česko Jihovýchod Jihomoravský kraj Activity type Higher or Secondary Education Establishments Administrative Contact Irena čornejová (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data