Results obtained during the research include the following: (1) the historical premises of the homotopy type theory and the univalent approach to the foundations of mathematics were considered; (2) the philosophical meaning of the homotopy type theory was investigated, also it was contrasted with other variants of type theory; (3) the philosophical premises, the meaning and consequences of the univalence axiom was investigated, (4) the ontological status of objects of mathematics is defined and investigated from the point of view of a univalent approach, (5) relevant methods of mathematical objects research from the point of view of a unified approach were studied, (6) the philosophical and methodological foundations and principles of further research within the framework of a univalent approach to the foundations of mathematics were formulated and studied.
|有效的开始/结束日期||01/01/2016 → 31/12/2017|
Type of Financial Sources
- Presidential Grant
UrFU Research Division section that handles this grant (Kuibyshev, Mira)
- Kuibyshev Research Division