Now showing items 1-20 of 23

    • A Cartan-Eilenberg approach to homotopical algebra 

      Pascual Gainza, Pere; Roig Martí, Agustín; Guillén Santos, Francisco; Navarro Aznar, Vicente (2008-09-01)
      Article
      Open Access
      In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects ...
    • A Cartan-Eilenberg approach to homotopical algebra 

      Guillén Santos, Francisco; Navarro Aznar, Vicente; Pascual Gainza, Pere; Roig Martí, Agustín (2010)
      Article
      Restricted access - publisher's policy
      In this paper we propose an approach to homotopical algebra w here the basic ingredient is a category with two classes of distinguished morphisms: s trong and weak equivalences. These data determine the cofibrant objects ...
    • André spectral sequences for Baues-Wirsching cohomology of categories 

      Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew (2011-12-16)
      Other
      Open Access
      We construct spectral sequences in the framework of Baues-Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications ...
    • André spectral sequences for Baues–Wirsching cohomology of categories 

      Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew (2012-04-30)
      Article
      Restricted access - publisher's policy
      We construct spectral sequences in the framework of Baues–Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications ...
    • Bass numbers of local cohomology of cover ideals of graphs 

      Álvarez Montaner, Josep; Sohrabi, Fatemeh (2020)
      Article
      Open Access
      We develop splitting techniques to study the Lyubeznik numbers of cover ideals of graphs which allow us to describe them for large families of graphs including forests, cycles, wheels and cactus graphs. More generally, we ...
    • Bass numbers of local cohomology of cover ideals of graphs 

      Álvarez Montaner, Josep; Sohrabi, Fatemeh (2019)
      External research report
      Open Access
      We develop splitting techniques to study Lyubeznik numbers of cover ideals of graphs which allow us to describe them for large families of graphs including forests, cycles, wheels and cactus graphs. More generally we are ...
    • Cartan-Eilenberg categories and descent categories 

      Pascual Gainza, Pere (2009-09)
      External research report
      Open Access
      Contents 1. Introduction 2. Remarks on localization of categories 3. Co¯brant objects 4. Cartan-Eilnberg categories 5. Minimal models: Sullivan categories 6. Models of functors 7. Cotriples and Cartan-Eilenberg categories
    • Cell-sets and decomposition spaces 

      Galve Regolf, Sergi (Universitat Politècnica de Catalunya, 2020-10)
      Master thesis
      Open Access
      This project, termed Cell Sets and Decomposition Spaces, is an introduction to the connections between homotopy and algebraic combinatorics. The main goal is to understand the category Cell of cell-sets and cell-maps, ...
    • Colored spanning graphs for set visualization 

      Hurtado Díaz, Fernando Alfredo; Korman, Matias; Van Kreveld, Matias; Löffler, Maarten; Sacristán Adinolfi, Vera; Shioura, Akiyoshi; Silveira, Rodrigo Ignacio; Speckmann, Bettina; Tokuyama, Takeshi (2018-03)
      Article
      Open Access
      We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the ...
    • Estructuras A-infinito en la opérada de cactus 

      Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew (2012)
      Conference lecture
      Restricted access - publisher's policy
      Diversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una ...
    • Extensions of groups 

      Ruiz Herrero, Víctor (Universitat Politècnica de Catalunya, 2018-07)
      Bachelor thesis
      Open Access
      A study of extensions of groups: given 2 groups G and K, I study the groups E that have K as a normal subgroup such that G = E/K. It is related with exact sequences and group cohomology.
    • Godement resolution and operad sheaf homotopy theory 

      Rodríguez González, Beatriz; Roig Martí, Agustín (2017-08-08)
      Article
      Open Access
      We show how to induce products in sheaf cohomology for a wide variety of coefficients: sheaves of dg commutative and Lie algebras, symmetric Omega-spectra, filtered dg algebras, operads and operad algebras.
    • Homotopy Batalin-Vilkovisky Algebras 

      Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Vallette, Bruno (2012)
      Article
      Open Access
      This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define ...
    • Homotopy Batalin-Vilkovisky algebras 

      Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Vallette, Bruno (2011-03-30)
      Other
      Open Access
      This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define ...
    • Homotopy linear algebra 

      Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2016-02)
      External research report
      Open Access
      By homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices ...
    • Homotopy linear algebra 

      Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew (2018-04)
      Article
      Open Access
      By homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices ...
    • Local cohomology supported on monomial ideals 

      Álvarez Montaner, Josep (2013-09-02)
      Article
      Restricted access - publisher's policy
    • Model categories and cubical descent 

      Rubió Pons, Llorenç (2007-06-12)
      Article
      Open Access
      We prove that the subcategory of fibrant objects of a simplicial model category is a cohomological descent category, in the sense of Guillén and Navarro, if and only if an acyclicity criterion holds.
    • Pruned cellular free resolutions of monomial ideals 

      Álvarez Montaner, Josep; Fernández Ramos, Óscar; Gimenez, Philippe (2020-01-01)
      Article
      Restricted access - publisher's policy
      Using discrete Morse theory, we give an algorithm that prunes the excess of information in the Taylor resolution and constructs a new cellular free resolution for an arbitrary monomial ideal. The pruned resolution is not ...
    • Some remarks on Cartan-Eilenberg categories 

      Pascual Gainza, Pere (2012-05)
      Article
      Restricted access - publisher's policy
      In this note we collect some remarks and examples on Cartan–Eilenberg categories.