Search for dissertations about: "Category theory"

Showing result 1 - 5 of 181 swedish dissertations containing the words Category theory.

2. 1. Homotopy Theory and TDA with a View Towards Category Theory

   Author : Sebastian Öberg; Wojciech Chachólski; David Blanc; KTH; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Homotopy theory; Topological Data Analysis; Category theory; Mapping spaces; Homotopy commutative diagrams; Matematik; Mathematics;

   Abstract : This thesis contains three papers. Paper A and Paper B deal with homotopy theory and Paper C deals with Topological Data Analysis. All three papers are written from a categorical point of view.In Paper A we construct categories of short hammocks and show that their weak homotopy type is that of mapping spaces. READ MORE

4. 2. Relations in Dependent Type Theory

   Author : Carlos Gonzalía; Göteborgs universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; formalized mathematics; relational systems; category theory; programming logics; constructive type theory; logical frameworks; relational database model;

   Abstract : This thesis investigates how to express and reason about relational concepts and methods inside the constructive logical framework of Martin-Löf's monomorphic type theory. We cover several areas where the notion of relation is central, and show how to formalize the basic concepts of each area. READ MORE

5. 3. Localic Categories of Models and Categorical Aspects of Intuitionistic Ramified Type Theory

   Author : Johan Lindberg; Erik Palmgren; Peter LeFanu Lumsdaine; Henrik Forssell; Benno van den Berg; Stockholms universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Topos theory; predicative topos theory; ramified type theory; type theory; localic groupoids; Mathematics; matematik;

   Abstract : This thesis contains three papers, all in the general area of categorical logic, together with an introductory part with some minor results and proofs of known results which does not appear to be (easily) available in the literature.In Papers I and II we investigate the formal system Intuitionistic Ramified Type Theory (IRTT), introduced by Erik Palmgren, as an approach to predicative topos theory. READ MORE

6. 4. Hopf and Frobenius algebras in conformal field theory

   Author : Carl Stigner; Jürgen Fuchs; Jens Fjelstad; Ingo Runkel; Karlstads universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; conformal field theory; category theory; Hopf algebra; Frobenius algebra; coends; mapping class group; defect lines; factorization constraints; Physics; Fysik;

   Abstract : There are several reasons to be interested in conformal field theories in two dimensions. Apart from arising in various physical applications, ranging from statistical mechanics to string theory, conformal field theory is a class of quantum field theories that is interesting on its own. First of all there is a large amount of symmetries. READ MORE

7. 5. A Proof and Formalization of the Initiality Conjecture of Dependent Type Theory

   Author : Menno de Boer; Peter LeFanu Lumsdaine; Alexander Berglund; Bas Spitters; Stockholms universitet; []
   Keywords : NATURVETENSKAP; NATURAL SCIENCES; Dependent type theory; Category theory; Contextual categories; Initiality; Formalization; Mathematics; matematik; matematisk logik; Mathematical Logic;

   Abstract : In this licentiate thesis we present a proof of the initiality conjecture for Martin-Löf’s type theory with 0, 1, N, A+B, ∏AB, ∑AB, IdA(u,v), countable hierarchy of universes (Ui)iєN closed under these type constructors and with type of elements (ELi(a))iєN. We employ the categorical semantics of contextual categories. READ MORE