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Categories (Mathematics)

  • An invitation to general algebra and universal constructionsby George M. Bergman

    Springer International Publishing 2015; US$ 89.99

    Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation... more...

  • Index Analysisby Robert Lowen

    Springer London 2015; US$ 129.00

    The featured review of the AMS describes the author?s earlier work in the field of approach spaces as, ?A landmark in the history of general topology?. In this book, the author has expanded this study further and taken it in a new and exciting direction. The number of conceptually and technically different systems which characterize approach spaces... more...

  • Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spacesby Marek Golasinski; Juno Mukai

    Springer International Publishing 2014; US$ 89.99

    This is a monograph that details the use of Siegel?s method and the classical results of homotopy groups of spheres and Lie groups to determine some Gottlieb groups of projective spaces or to give the lower bounds of their orders. Making use of the properties of Whitehead products, the authors also determine some Whitehead center groups of projective... more...

  • Homological Mirror Symmetry and Tropical Geometryby Ricardo Castano-Bernard; Fabrizio Catanese; Maxim Kontsevich; Tony Pantev; Yan Soibelman; Ilia Zharkov

    Springer International Publishing 2014; US$ 59.99

    The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the ?tropical? approach to Gromov-Witten theory and the work... more...

  • Triangulated Categories. (AM-148)by Amnon Neeman

    Princeton University Press 2014; US$ 97.50

    The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research, providing, among... more...

  • Representation Theoryby Alexander Zimmermann

    Springer 2014; US$ 149.00

    Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory.... more...

  • Topoiby R. Goldblatt

    Elsevier Science 2014; US$ 72.95

    The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the... more...

  • Axiomatic Method and Category Theoryby Andrei Rodin

    Springer 2013; US$ 129.00

    This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method,... more...

  • Homological Algebraby Marco Grandis

    World Scientific Publishing Company 2013; US$ 166.00

    We propose here a study of ‘semiexact’ and ‘homological' categories as a basis for a generalised homological algebra. Our aim is to extend the homological notions to deeply non-abelian situations, where satellites and spectral sequences can still be studied.This is a sequel of a book on ‘Homological Algebra, The interplay of... more...

  • Homological Algebraby Marco Grandis

    World Scientific Publishing Company 2012; US$ 166.00

    In this book we want to explore aspects of coherence in homological algebra, that already appear in the classical situation of abelian groups or abelian categories. Lattices of subobjects are shown to play an important role in the study of homological systems, from simple chain complexes to all the structures that give rise to spectral sequences. A... more...