Now showing items 1-20 of 21

• #### A brief introduction to synthetic differential geometry ﻿

(Universitat Politècnica de Catalunya, 2017-09)
Bachelor thesis
Open Access
The 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 topos-theoretic framework. Though ...
• #### A Cartan-Eilenberg approach to homotopical algebra ﻿

(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 Categorical approach to Tannaka Duality ﻿

(Universitat Politècnica de Catalunya, 2016-07)
Master thesis
Open Access
The aim of this work is to study, in a categorical context, similar results to the Tannaka-Krein 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 ﻿

(2015-11-01)
Article
Open Access
The dg operad of cellular chains on the operad of spineless cacti of Kaufmann (Topology 46(1):39-88, 2007) is isomorphic to the Gerstenhaber-Voronov dg operad codifying the cup product and brace operations on the Hochschild ...
• #### An A-infinity operad in spineless cacti ﻿

(2015-04-17)
External research report
Open Access
The d.g. operad C of cellular chains on the operad of spineless cacti is isomorphic to the Gerstenhaber-Voronov 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 ﻿

(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 ...
• #### Cell-sets and decomposition spaces ﻿

(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, ...
• #### Decomposition spaces in combinatorics ﻿

(2016-12)
External research report
Open Access
A decomposition space (also called unital 2-Segal 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, 2021-07)
Master thesis
Open Access
The Brunel network is a neuronal network model composed of excitatory and inhibitory leaky integrate-and-fire spiking neurons. This network is known to present four distinguished activity states, which can be mainly described ...
• #### Extensions of groups ﻿

(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.
• #### Gabriel–Zisman cohomology and spectral sequences ﻿

(Springer Nature, 2021-02-10)
Article
Restricted access - publisher's policy
Extending 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, Stark-Heegner points and diagonal classes ﻿

(2020-02-03)
Book
Restricted access - publisher's policy
• #### Homotopy Batalin-Vilkovisky Algebras ﻿

(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 ...
• #### Moduli spaces and formal operads ﻿

(2003)
Article
Open Access
Let 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 2-group ﻿

(2010-12-01)
External research report
Open Access
The regular representation of an essentially finite 2-group $\mathbb{G}$ in the 2-category $\mathbf{2Vect}_k$ of (Kapranov and Voevodsky) 2-vector spaces is defined and cohomology invariants classifying it computed. It is ...
• #### On the regular representation of an (essentially) finite 2-group ﻿

(2011-05-01)
Article
Restricted access - publisher's policy
The regular representation of an essentially finite 2-group $\mathbb{G}$ in the 2-category $\mathbf{2Vect}_k$ of (Kapranov and Voevodsky) 2-vector spaces is defined and cohomology invariants classifying it computed. It is ...
• #### On the representations of 2-groups in Baez-Crans 2-vector spaces ﻿

(2016-10-06)
Article
Open Access
We study the theory of representations of a 2-group G in Baez-Crans 2-vector spaces over a field k of arbitrary characteristic, and the corresponding 2-vector spaces of intertwiners. We also characterize the irreducible ...
• #### Review of the book: "Category Theory" ﻿

(2010)
External research report
Open Access
Book 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, 2021-07)
Master thesis
Restricted access - author's decision
In 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, 2015-05)
Bachelor thesis
Open Access
The 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 ...