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,

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Identity

There exists an identity element denoted $$e_G$$ for $$\bullet$$,

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Inverse
Every element of $$G$$ has an inverse with respect to $$\bullet$$,

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