Sökning: "Sebastian Öberg"

Hittade 2 avhandlingar innehållade orden Sebastian Öberg.

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

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

   Sammanfattning : 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. LÄS MER

3. 2. Modeling mapping spaces with short hammocks

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

   Sammanfattning : 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. LÄS MER