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[null,"1.","Record Nr.",null,"UNINA9910151928803321"]
[null,null,"Autore",null,"Brown Ronald"]
[null,null,"Titolo",null,"Nonabelian Algebraic Topology [[electronic resource] ] : Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids / / Ronald Brown, Philip J. Higgins, Rafael Sivera"]
[null,null,"Pubbl/distr/stampa",null,"Zuerich, Switzerland, : European Mathematical Society Publishing House, 2011"]
[null,null,"ISBN",null,"3-03719-583-5"]
[null,null,"Descrizione fisica",null,"1 online resource (703 pages)"]
[null,null,"Collana",null,"EMS Tracts in Mathematics (ETM) ; 15"]
[null,null,"Classificazione",null,"55-xx18-xx"]
[null,null,"Soggetti",null,"Algebraic topology"]
[{"$nulls":4},"Category theory; homological algebra"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Sommario/riassunto","The main theme of this book is that the use of filtered spaces rather than  just topological spaces allows the development of basic algebraic topology in  terms of higher homotopy groupoids; these algebraic structures better  reflect the geometry of subdivision and composition than those commonly in  use. Exploration of these uses of higher dimensional versions of groupoids  has been largely the work of the first two authors since the mid 1960s.    The structure of the book is intended to make it useful to a wide class of  students and researchers for learning and evaluating these methods, primarily  in algebraic topology but also in higher category theory and its applications  in analogous areas of mathematics, physics and computer science.  Part I explains the intuitions and theory in dimensions 1 and 2, with many  figures and diagrams, and a detailed account of the theory of crossed  modules. Part II develops the applications of crossed complexes. The engine  driving these applications is the work of Part III on cubical ω-groupoids,  their relations to crossed complexes, and their homotopically defined examples  for filtered spaces. Part III also includes a chapter suggesting further  directions and problems, and three appendices give accounts of some  relevant aspects of category theory. Endnotes for each chapter give further  history and references."]