English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The paper considers non-Abelian homology groups for a diagram of groupsintroduced as homotopy groups of a simplicial replacement. It is proved thatthe non-Abelian homology groups of the group diagram are isomorphic to thehomotopy groups of the homotopy colimit of the diagram of classifying spaces,with a dimension shift of 1. As an application, a method is developed forfinding a nonzero homotopy group of least dimension for a homotopy colimit ofclassifying spaces. For a group diagram over a free category with a zerocolimit, a criterion for the isomorphism of the first non-Abelian and firstAbelian homology groups is obtained. It is established that the non-Abelianhomology groups are isomorphic to the cotriple derived functors of the colimitfunctor defined on the category of group diagrams.

Non-Abelian homology and homotopy colimit of classifying spaces for a diagram of groups