Browsing by Subject "Categories (Matemàtica)"
Now showing items 120 of 21

A brief introduction to synthetic differential geometry
(Universitat Politècnica de Catalunya, 201709)
Bachelor thesis
Open AccessThe goal of this thesis is to explore the basic axiomatic theory of Syn thetic Differential Geometry (SDG). This field aims to put the study of smooth manifolds, and geometry therein, in a topostheoretic framework. Though ... 
A CartanEilenberg approach to homotopical algebra
(20080901)
Article
Open AccessIn 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 Categorical approach to Tannaka Duality
(Universitat Politècnica de Catalunya, 201607)
Master thesis
Open AccessThe aim of this work is to study, in a categorical context, similar results to the TannakaKrein duality theorem. We prove a reconstruction theorem which allows one to recover a given group G as the monoid of natural ... 
An A(infinity)Operad in Spineless Cacti
(20151101)
Article
Open AccessThe dg operad of cellular chains on the operad of spineless cacti of Kaufmann (Topology 46(1):3988, 2007) is isomorphic to the GerstenhaberVoronov dg operad codifying the cup product and brace operations on the Hochschild ... 
An Ainfinity operad in spineless cacti
(20150417)
External research report
Open AccessThe d.g. operad C of cellular chains on the operad of spineless cacti is isomorphic to the GerstenhaberVoronov operad codifying the cup product and brace operations on the Hochschild cochains of an associative algebra, ... 
André spectral sequences for Baues–Wirsching cohomology of categories
(20120430)
Article
Restricted access  publisher's policyWe 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 ... 
Cellsets and decomposition spaces
(Universitat Politècnica de Catalunya, 202010)
Master thesis
Open AccessThis 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 cellsets and cellmaps, ... 
Decomposition spaces in combinatorics
(201612)
External research report
Open AccessA decomposition space (also called unital 2Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to homotopy) composition, the new ... 
Detection of dynamical states of neuronal networks with persistent homology tools
(Universitat Politècnica de Catalunya, 202107)
Master thesis
Open AccessThe Brunel network is a neuronal network model composed of excitatory and inhibitory leaky integrateandfire spiking neurons. This network is known to present four distinguished activity states, which can be mainly described ... 
Extensions of groups
(Universitat Politècnica de Catalunya, 201807)
Bachelor thesis
Open AccessA 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. 
Gabriel–Zisman cohomology and spectral sequences
(Springer Nature, 20210210)
Article
Restricted access  publisher's policyExtending constructions by Gabriel and Zisman, we develop a functorial framework for the cohomology and homology of simplicial sets with very general coefficient systems given by functors on simplex categories into abelian ... 
Heegner points, StarkHeegner points and diagonal classes
(20200203)
Book
Restricted access  publisher's policy 
Homotopy BatalinVilkovisky Algebras
(2012)
Article
Open AccessThis paper provides an explicit cofibrant resolution of the operad encoding BatalinVilkovisky algebras. Thus it defines the notion of homotopy BatalinVilkovisky algebras with the required homotopy properties. To define ... 
Moduli spaces and formal operads
(2003)
Article
Open AccessLet Mg,l be the moduli space of stable algebraic curves of genus g with l marked points. With the operations which relate the different moduli spaces identifying marked points, the family (Mg,l)g,l is a modular operad ... 
On the regular representation of an (essentially) finite 2group
(20101201)
External research report
Open AccessThe regular representation of an essentially finite 2group $\mathbb{G}$ in the 2category $\mathbf{2Vect}_k$ of (Kapranov and Voevodsky) 2vector spaces is defined and cohomology invariants classifying it computed. It is ... 
On the regular representation of an (essentially) finite 2group
(20110501)
Article
Restricted access  publisher's policyThe regular representation of an essentially finite 2group $\mathbb{G}$ in the 2category $\mathbf{2Vect}_k$ of (Kapranov and Voevodsky) 2vector spaces is defined and cohomology invariants classifying it computed. It is ... 
On the representations of 2groups in BaezCrans 2vector spaces
(20161006)
Article
Open AccessWe study the theory of representations of a 2group G in BaezCrans 2vector spaces over a field k of arbitrary characteristic, and the corresponding 2vector spaces of intertwiners. We also characterize the irreducible ... 
Review of the book: "Category Theory"
(2010)
External research report
Open AccessBook Review Category Theory, Second Edition Steve Awodey Oxford Logic Studies 52. Oxford University Press, 2010. ISBN 978 0 19 958736 0 
Tannakian categories, Galois connections and decomposition spaces
(Universitat Politècnica de Catalunya, 202107)
Master thesis
Restricted access  author's decisionIn this thesis, we want to present the basic theory of tensor categories in order to give a precise statement of what is a neutral Tannakian category, which is the simplest notion of Tannakian category. After that, we give ... 
Topological quantum field theories
(Universitat Politècnica de Catalunya, 201505)
Bachelor thesis
Open AccessThe aim of this work is to explain what a topological quantum field theory (TQFT) is and the relation between TQFTs in dimension 2 and Frobenius algebras. More precisely, it is shown that there exists an equivalence of ...