The proposed programme of research will develop a comprehensive theory of models for two extensions of classical dependent type theory: dependent type theory with non-extensional equality, and linear dependent type theory.
It will do this by altering the existing theory of models for dependent types in two fundamental ways: firstly, by shifting from one-dimensional to higher-dimensional categories, and secondly, by shifting from cartesian structures to monoidal strucures.
It will then look for applications for this generalised theory in, amongst other areas, categorical logic, homotopy theory and quantum computing This programme will be implemented by the Fellow working in close collaboration with members of the host organisation; the Fellow will bring skill s and experience in the area of higher-dimensional category theory, enriched category theory, and linear logic; the host organisation, skills and experience in dependent type theory.
This project fits tightly with the objectives of the Specific Programme o f the EIF and the broader Human Resources and Mobility Work Programme, by providing the Fellow with an opportunity to undergo training through research, thereby diversifying his technical expertise from higher-dimensional category theory to the complementary area of dependent type theory and its applications in theoretical computer science.
By providing him with the opportunity to relocate from the UK to Uppsala, Sweden, it will allow this training to take place in the location most suitable for his needs, namely at an internationally recognised centre of excellence in dependent type theory.
Moreover, by promoting a cross-fertilisation of the still distinct disciplines of categorical logic and dependent type theory, it will lead to the development of a new area of research and the creation of European centres of excellence in this new area, thereby increasing Europe and competitiveness and attractiveness to researchers in the field.
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