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 \( \bullet \),[\[ ? \]]