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Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups. (English) Zbl 1030.55013
A crossed complex is an abstract version of the collection of $$E_{1}$$ terms of the homology spectral sequence for a CW complex, one for each element of the space, and where one keeps track of the action of the fundamental groupoid. The authors give a precise definition and then display examples of these objects in topology and group theory.

##### MSC:
 55U05 Abstract complexes in algebraic topology 18G50 Nonabelian homological algebra (category-theoretic aspects) 18G10 Resolutions; derived functors (category-theoretic aspects)
##### Keywords:
crossed complex; homotopy pushouts
groupoids; Gpd
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