Matches in DBpedia 2016-04 for { ?s ?p "In foundations of mathematics, univalent foundations is an approach to the foundations of constructive mathematics based on the idea that mathematics studies structures on \"univalent types\" that correspond, under the projection to set-theoretic mathematics, to homotopy types. Univalent foundations are inspired both by the old Platonic ideas of Hermann Grassmann and Georg Cantor and by the \"categorical\" mathematics in the style of Alexander Grothendieck. It departs from the use of predicate logic as the underlying formal deduction system, replacing it, at the moment, by a version of the Martin-Löf type theory. The development of the univalent foundations is closely related with the development of homotopy type theory.Univalent foundations are compatible with structuralism, if an appropriate (i.e. categorical) notion of mathematical structure is adopted."@en }
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- Univalent_foundations abstract "In foundations of mathematics, univalent foundations is an approach to the foundations of constructive mathematics based on the idea that mathematics studies structures on \"univalent types\" that correspond, under the projection to set-theoretic mathematics, to homotopy types. Univalent foundations are inspired both by the old Platonic ideas of Hermann Grassmann and Georg Cantor and by the \"categorical\" mathematics in the style of Alexander Grothendieck. It departs from the use of predicate logic as the underlying formal deduction system, replacing it, at the moment, by a version of the Martin-Löf type theory. The development of the univalent foundations is closely related with the development of homotopy type theory.Univalent foundations are compatible with structuralism, if an appropriate (i.e. categorical) notion of mathematical structure is adopted.".