Search for dissertations about: "Sebastian Öberg"

Found 2 swedish dissertations containing the words Sebastian Öberg.

  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. Modeling mapping spaces with short hammocks

    Author : Sebastian Öberg; Wojciech Chachólski; Fernando Muro; KTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Mapping spaces; hammocks; homotopy theory; category theory; Matematik; Mathematics;

    Abstract : We construct a category of short hammocks and show that it has the weak homotopy type of mapping spaces. In doing so we tackle the problem of applying the nerve to large categories without the use of multiple universes. We also explore what the mapping space is. READ MORE