Search for dissertations about: "Constructive mathematics"
Showing result 11 - 15 of 20 swedish dissertations containing the words Constructive mathematics.
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11. Representation theorems for abelian and model categories
Abstract : In this PhD thesis we investigate a representation theorem for small abelian categories and a representation theorem for left proper, enriched model categories, with the purpose of describing them concretely in terms of specific well-known categories.For the abelian case, we study the constructivity issues of the Freyd-Mitchell Embedding Theorem, which states the existence of a full embedding from a small abelian category into the category of modules over an appropriate ring. READ MORE
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12. Exact completion and type-theoretic structures
Abstract : This thesis consists of four papers and is a contribution to the study of representations of extensional properties in intensional type theories using, mainly, the language and tools from category theory. Our main focus is on exact completions of categories with weak finite limits as a category-theoretic description of the setoid construction in Martin-Löf's intensional type theory. READ MORE
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13. A Natural Interpretation of Classical Proofs
Abstract : In this thesis we use the syntactic-semantic method of constructive type theory to give meaning to classical logic, in particular Gentzen's LK.We interpret a derivation of a classical sequent as a derivation of a contradiction from the assumptions that the antecedent formulas are true and that the succedent formulas are false, where the concepts of truth and falsity are taken to conform to the corresponding constructive concepts, using function types to encode falsity. READ MORE
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14. Formalizing Refinements and Constructive Algebra in Type Theory
Abstract : The extensive use of computers in mathematics and engineering has led to an increased demand for reliability in the implementation of algorithms in computer algebra systems. One way to increase the reliability is to formally verify that the implementations satisfy the mathematical theorems stating their specification. READ MORE
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15. 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