Note that in the category of monoids, category-theoretic kernels exist just as for groups, but these kernels don't carry sufficient information for algebraic purposes. Therefore, the notion of kernel studied in monoid theory is slightly different (see #Relationship to algebraic kernels below).
Note that in the category of monoids, category-theoretic kernels exist just as for groups but these kernels don't carry sufficient information for algebraic purposes. Therefore, the notion of kernel studied in monoid theory is slightly different (see #Relationship to algebraic kernels below).