a:

Unit holds because \\(0 + m = m \\) and \\(m + 0 = m \\),

associativity holds because \\((m_1 + m_2) + m_3 = m_1 + (m_2 + m_3) \\)

b:

Unit holds because \\([] ++ m = m \\) and \\( m ++ [] = m \\)

associativity holds because \\((m_1 ++ m_2) ++ m_3 = m_1 ++ (m_2 ++ m_3) \\)

c:

A monoid can be viewed as a category with a single object (call it obj)

with the set of morphisms C(obj, obj) = M

the function * gives us the composition rule

and e in M gives us the identity morphism.

The Unit and associative laws of the Moniod correspond to the unit and associative laws of the category.

Unit holds because \\(0 + m = m \\) and \\(m + 0 = m \\),

associativity holds because \\((m_1 + m_2) + m_3 = m_1 + (m_2 + m_3) \\)

b:

Unit holds because \\([] ++ m = m \\) and \\( m ++ [] = m \\)

associativity holds because \\((m_1 ++ m_2) ++ m_3 = m_1 ++ (m_2 ++ m_3) \\)

c:

A monoid can be viewed as a category with a single object (call it obj)

with the set of morphisms C(obj, obj) = M

the function * gives us the composition rule

and e in M gives us the identity morphism.

The Unit and associative laws of the Moniod correspond to the unit and associative laws of the category.