Cosimplicial group

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QUICK PHRASES: cosimplicial object in category of groups, group object in category of cosimplicial sets

Definition

Abstract definition

A cosimplicial group can be defined in the following equivalent ways:

  1. Explicitly, it is a covariant functor from the simplex category to the category of groups.
  2. It is a cosimplicial object in the category of groups.
  3. It is a group object in the category of cosimplicial sets.

Related notions