# Complete (mathematics)

From Ref

The term *complete* in mathematics is used in the following broad senses:

- An algebraic, topological or geometric structure that is closed under certain kinds of operations.
- A structure such that any bigger structure containing it has it as a
*summand*or*split piece*.

## Contents

### In group theory

**Complete group**: A group whose center is trivial and in which every automorphism is inner. Equivalently, it is a direct factor inside any group in which it is a normal subgroup.

Primary subject wiki entry: Groupprops:Complete group

### In category theory

**Complete category**: A category that contains all small limits.

Primary subject wiki entry: Cattheory:Complete category