Exploració per tema "Categories (Mathematics)"
Ara es mostren els items 1-20 de 26
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A brief introduction to synthetic differential geometry
(Universitat Politècnica de Catalunya, 2017-09)
Treball Final de Grau
Accés obertThe 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 Categorical approach to Tannaka Duality
(Universitat Politècnica de Catalunya, 2016-07)
Projecte Final de Màster Oficial
Accés obertThe 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
Accés obertThe 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)
Report de recerca
Accés obertThe 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
Accés restringit per política de l'editorialWe 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)
Projecte Final de Màster Oficial
Accés obertThis 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)
Report de recerca
Accés obertA 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)
Projecte Final de Màster Oficial
Accés obertThe 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 ... -
Equivalència de Morita
(Universitat Politècnica de Catalunya, 2019-07)
Treball Final de Grau
Accés obertL'estudi de la teoria d'anells està intimament lligada a l'anàlisi de les categories de mòduls sobre un anell. En particular, bona part de l'àlgebra homològica depèn exclusivament de la categoria de mòduls sobre R. El ... -
Extensions of groups
(Universitat Politècnica de Catalunya, 2018-07)
Treball Final de Grau
Accés obertA 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
Accés obertExtending 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 ... -
General persistence theory: on the course to multiparameter persistent homology
(Universitat Politècnica de Catalunya, 2022-10)
Projecte Final de Màster Oficial
Accés obertWe explore Persistence Theory in its full generality. As a particular instance, we first discuss one parameter persistence theory, which arises from uniparametric filtrations of spaces. Although enjoying many excellent ... -
Heegner points, Stark-Heegner points and diagonal classes
(2020-02-03)
Llibre
Accés restringit per política de l'editorial -
Homotopy Batalin-Vilkovisky Algebras
(2012)
Article
Accés obertThis 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 ... -
Improving neural networks using topological data analysis
(Universitat Politècnica de Catalunya, 2022-09)
Projecte Final de Màster Oficial
Accés obertGeneralisation measures are metrics that indicate how well a neural network will perform in presence of unknown data. Differentiable generalisation measures with respect to the parameters of a neural network that use only ... -
Moduli spaces and formal operads
(2003)
Article
Accés obertLet 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)
Report de recerca
Accés obertThe 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
Accés restringit per política de l'editorialThe 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
Accés obertWe 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)
Report de recerca
Accés obertBook Review Category Theory, Second Edition Steve Awodey Oxford Logic Studies 52. Oxford University Press, 2010. ISBN 978 0 19 958736 0
