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Maria Manuel Clementino - New Perspectives in Algebra, Topology and Categories: Summer School, Louvain-la-Neuve, Belgium, September 12-15, 2018 and September 11-14, 2019

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Maria Manuel Clementino New Perspectives in Algebra, Topology and Categories: Summer School, Louvain-la-Neuve, Belgium, September 12-15, 2018 and September 11-14, 2019

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This book provides an introduction to some key subjects in algebra and topology. It consists of comprehensive texts of some hours courses on the preliminaries for several advanced theories in (categorical) algebra and topology. Often, this kind of presentations is not so easy to find in the literature, where one begins articles by assuming a lot of knowledge in the field. This volume can both help young researchers to quickly get into the subject by offering a kind of roadmap and also help master students to be aware of the basics of other research directions in these fields before deciding to specialize in one of them. Furthermore, it can be used by established researchers who need a particular result for their own research and do not want to go through several research papers in order to understand a single proof. Although the chapters can be read as self-contained chapters, the authors have tried to coordinate the texts in order to make them complementary.
The seven chapters of this volume correspond to the seven courses taught in two Summer Schools that took place in Louvain-la-Neuve in the frame of the project Fonds dAppui lInternationalisation of the Universit catholique de Louvain to strengthen the collaborations with the universities of Coimbra, Padova and Poitiers, within the Coimbra Group.

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Book cover of New Perspectives in Algebra Topology and Categories Volume 1 - photo 1
Book cover of New Perspectives in Algebra, Topology and Categories
Volume 1
Coimbra Mathematical Texts
Series Editors
Ana Paula Santana
Department of Mathematics, University of Coimbra, Coimbra, Portugal
Jlio S. Neves
Department of Mathematics, University of Coimbra, Coimbra, Portugal
Marcelo Viana
IMPA, Rio de Janeiro, Brazil
Maria Paula Serra de Oliveira
Department of Mathematics, University of Coimbra, Coimbra, Portugal
Rui Loja Fernandes
Department of Mathematics, University of Illinois, Urbana, IL, USA

More information about this series at http://www.springer.com/series/16723

Editors
Maria Manuel Clementino , Alberto Facchini and Marino Gran
New Perspectives in Algebra, Topology and Categories
Summer School, Louvain-la-Neuve, Belgium, September 1215, 2018 and September 1114, 2019
1st ed. 2021
Logo of the publisher Editors Maria Manuel Clementino Departamento de - photo 2
Logo of the publisher
Editors
Maria Manuel Clementino
Departamento de Matemtica, Universidade de Coimbra, Coimbra, Portugal
Alberto Facchini
Dipartimento di Matematica, Universit di Padova, Padova, Italy
Marino Gran
Institut de Recherche en Mathmatique et Physique, Universit catholique de Louvain, Louvain-la-Neuve, Belgium
Coimbra Mathematical Texts
ISBN 978-3-030-84318-2 e-ISBN 978-3-030-84319-9
https://doi.org/10.1007/978-3-030-84319-9
Mathematics Subject Classication (2010): 08A30 16-01 16B50 16S90 18A20 18E13 18E08 18B10 06D22 18F70 18A32 20M14 17-01 54H11 22-01
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG

The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Editors Preface

This book is addressed to a new generation of students and researchers in algebra, topology and category theory who are willing to learn the fundamental notions and principles of some of the active research fields in these areas.

The content of each of the seven chapters of this book fully covers the corresponding specialized course that was taught at the international Summer Schools in Algebra and Topology. The schools were hosted by the Institut de Recherche en Mathmatique et Physique (IRMP) of the Universit catholique de Louvain (UCLouvain) in September 2018 and 2019.

These events were organized in the framework of a project Fonds dAppui lInternationalisation of the Universit catholique de Louvain together with the universities of Coimbra, Padova and Poitiers, aiming at strengthening the research collaborations in mathematics among institutions of the Coimbra Group. The speakers of the summer schools gave some introductory courses on various topics of interest related to their own research fields, addressed to an audience including both masters and PhD students and more experienced mathematicians who were interested in these subjects. The participants in the summer schools came from many different countries in Europe, North America and Asia.

These summer schools greatly facilitated scientific discussions leading to the development of new connections among the various concepts and theories presented during the lectures.

The main subjects in algebra and topology the reader will be introduced to in this volume are:
  • the theory of comodules and contramodules;

  • the theory of topological semi-abelian algebras;

  • the theories of commutative monoids and of non-commutative rings;

  • regular categories and the calculus of relations;

  • the categorical approach to commutator theory;

  • locale theory and the point-free perspective on topology;

  • the theory of non-associative algebras.

We are very grateful to the many colleagues who have contributed in making this project possible and successful. In particular, we would like to express our gratitude to
  • Ms. Dana Samson, Prorectrice linternational de lUCLouvain;

  • Ms. Ana Fernandez-Gacio, Coordinator of the international relations of the Science and Technology Sector of the UCLouvain;

  • Ms. Anne Querinjean, director of the Muse universitaire de Louvain;

  • Ms. Carine Baras, Secrtaire de recherche;

  • Ms. Martine Furnemont, Secrtaire of the IRMP;

  • Mr. Michel Devillers, Vice-rector of the Science and Technology Sector;

  • Mr. Tim van der Linden, Professor at the UCLouvain.

  • The editors of the Coimbra Mathematical Texts, Ana Paula Santana, Jlio S. Neves, Marcelo Viana, Maria Paula Serra de Oliveira and Rui Loja Fernandes.

The project leading to the publication of this book has been generously supported by the following institutions:
  • UCLouvain (via the Fonds dAppui lInternationalisation)

  • The Institut de Recherche en Mathmatique et Physique;

  • The Centre for Mathematics of the University of Coimbra;

  • the Coimbra Group;

  • the Ecole doctorale en Mathmatique du FNRS;

  • the Erasmus+ programme of the European Union.

Sincerely,

Maria Manuel Clementino
Alberto Facchini
Marino Gran
Preface to the Book Series Coimbra Mathematical Texts

This new Springer series Coimbra Mathematical Texts is a direct successor of a collection entitled Textos de Matemtica, published by the University of Coimbra, which started in 1993.

The aim of that collection was the publication of advanced mathematics texts resulting from events held at the University of CoimbraMathematics Department, and included conference proceedings as well as monographs related to graduate-level short courses. The first volume in the collection was Classical Invariants, by J. A. Green (1993), and the last one, no. 48, was 13th Young Researchers Workshop on Geometry, Mechanics and Control: three mini-courses (2019). The complete list of volumes, covering a wide range of mathematical topics, may be found at

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