Math and science::Algebra::Aluffi

# Group. Definition.

### Groups. Categorical definition.

A group is a [something with a what?].

More specifically, a group is the set [of what of a something].

Recall that a groupoid is a category where every morphism is an isomorphism.

Now the usual approach.

### Groups. Standard definition.

A group \( (G, \bullet) \) is a set \( G \) and a function \( \bullet : G \times G \to G \) (called a binary operation) where the following three properties are satisfied:

- Associativity
\( \bullet \) is associative,

[\[ ? \]]- Identity
There exists an identity element denoted \( e_G \) for \( \bullet \),

[\[ ? \]]- Inverse
- Every element of \( G \) has an inverse with respect to \( \bullet \),[\[ ? \]]