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New Perspectives in Algebra, Topology and Categories

Summer School, Louvain-la-Neuve, Belgium, September 12-15, 2018 and September 11-14, 2019

  • Provides an introduction to some key subjects in algebra and topology

  • Consists of comprehensive texts on the preliminaries for several advanced theories in algebra and topology

  • Helps young researchers to quickly get into the subject

Part of the book series: Coimbra Mathematical Texts (CMT, volume 1)

  • 2176 Accesses

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eBook USD 64.99
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  • ISBN: 978-3-030-84319-9
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  • Tax calculation will be finalised during checkout
Hardcover Book USD 84.99
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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xi
  2. An Invitation to Topological Semi-abelian Algebras

    • Maria Manuel Clementino
    Pages 27-66
  3. An Introduction to Regular Categories

    • Marino Gran
    Pages 113-145
  4. Categorical Commutator Theory

    • Sandra Mantovani, Andrea Montoli
    Pages 147-172
  5. Notes on Point-Free Topology

    • Jorge Picado, Aleš Pultr
    Pages 173-223
  6. Non-associative Algebras

    • Tim Van der Linden
    Pages 225-258

About this book

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 d’Appui à l’Internationalisation of the Université catholique de Louvain to strengthen the collaborations with the universities of Coimbra, Padova and Poitiers, within the Coimbra Group.

Keywords

  • Categorical Algebra
  • Category of Rings
  • Commutative Monoid
  • Commutator Theory
  • Frame
  • Homological Category
  • Locale, Non-associative Algebra
  • Normal Subobject
  • Point-free Topology
  • Regular Category
  • Semi-abelian Category
  • Split Extension
  • Topological Algebra
  • Universal Algebra

Editors and Affiliations

  • Departamento de Matematica, Universidade de Coimbra, Coimbra, Portugal

    Maria Manuel Clementino

  • Dipartimento di Matematica, University of Padova, Padua, Italy

    Alberto Facchini

  • Institut de Recherche en Mathématique et Physique, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Marino Gran

About the editors

Maria Manuel Clementino is a Professor at the Universidade de Coimbra in Portugal.

Alberto Facchini is a Professor at the University of Padova in Italy.

Marino Gran is a Professor at the Université catholique de Louvain in Belgium.

Bibliographic Information

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-030-84319-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book USD 84.99
Price excludes VAT (USA)