Search for dissertations about: "cubical sets"
Found 3 swedish dissertations containing the words cubical sets.
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1. A Model of Type Theory in Cubical Sets
Abstract : The intensional identity type is one if the most intricate concepts of dependent type theory. The recently discovered connection between homotopy theory and type theory gives a novel perspective on the identity type. READ MORE
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2. Cubical Intepretations of Type Theory
Abstract : The interpretation of types in intensional Martin-Löf type theory as spaces and their equalities as paths leads to a surprising new view on the identity type: not only are higher-dimensional equalities explained as homotopies, this view also is compatible with Voevodsky's univalence axiom which explains equality for type-theoretic universes as homotopy equivalences, and formally allows to identify isomorphic structures, a principle often informally used despite its incompatibility with set theory. While this interpretation in homotopy theory as well as the univalence axiom can be justified using a model of type theory in Kan simplicial sets, this model can, however, not be used to explain univalence computationally due to its inherent use of classical logic. READ MORE
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3. Formalizing Univalent Set-Level Structures in Cubical Agda
Abstract : This licentiate thesis consists of two papers on formalization projects using Cubical Agda, a rather new extension of the Agda proof assistant with constructive support for univalence and higher inductive types. The common denominator of the two papers is that they are concerned with structures on types that are sets in the sense of Homotopy Type Theory or Univalent Foundations (HoTT/UF). READ MORE
