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Crossed complexes and higher homotopy groupoids as noncommutative tools for higher dimensional local-to-global problems. (English) Zbl 1214.18014
Hazewinkel, M. (ed.), Handbook of algebra. Volume 6. Amsterdam: Elsevier/North-Holland (ISBN 978-0-444-53257-2/hbk). Handbook of Algebra 6, 83-124 (2009).
The author surveys and explains the origins of results obtained by himself, P. J. Higgins and others over the years 1974–2008 in basic algebraic topology on the border between homology and homotopy, using crossed complexes, rather than chain complexes, as a fundamental notion.
For the entire collection see [Zbl 1182.00007].

MSC:
18G55 Nonabelian homotopical algebra (MSC2010)
18G35 Chain complexes (category-theoretic aspects), dg categories
18-03 History of category theory
55-03 History of algebraic topology
01A60 History of mathematics in the 20th century
01A61 History of mathematics in the 21st century
55P65 Homotopy functors in algebraic topology
Software:
Gpd; GAP
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References:
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