Sökning: "homotopy algebra"

Visar resultat 1 - 5 av 31 avhandlingar innehållade orden homotopy algebra.

  1. 1. N-complexes and Categorification

    Författare :Djalal Mirmohades; Volodymyr Mazorchuk; Steffen Oppermann; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Homological algebra; Category theory; Triangulated categories; K-theory; Hopfological algebra; Mathematics; Matematik;

    Sammanfattning : This thesis consists of three papers about N-complexes and their uses in categorification. N-complexes are generalizations of chain complexes having a differential d satisfying dN = 0 rather than d2 = 0. Categorification is the process of finding a higher category analog of a given mathematical structure. LÄS MER

  3. 2. Representation theorems for abelian and model categories

    Författare :Anna Giulia Montaruli; Peter LeFanu Lumsdaine; Gregory Arone; Marek Zawadowski; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Category Theory; Logic; Algebra; Homotopy Theory; matematik; Mathematics;

    Sammanfattning : 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. LÄS MER

  4. 3. 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

  5. 4. Koszul duality for categories and a relative Sullivan-Wilkerson theorem

    Författare :Hadrien Espic; Gregory Arone; Alexander Berglund; Bjørn Dundas; Stockholms universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Koszul duality; categories; Yoneda algebra; operads; dg modules; homotopy automorphisms; Sullivan-Wilkerson; arithmetic group; matematik; Mathematics;

    Sammanfattning : This PhD thesis consists in a collection of three papers on Koszul duality of categories and on an analogue of the Sullivan-Wilkerson theorem for relative CW-complexes.In Paper I, we define a general notion of Koszul dual in the context of a monoidal biclosed model category. LÄS MER

  7. 5. 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