# Cosimplicial group

This is a variation of group|Find other variations of group | Read a survey article on varying group

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:

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