Generator (category theory)
From Wikipedia, the free encyclopedia
In category theory in mathematics a generator of a category 
is an object G of the category, such that for any two different morphisms 
in , there is a morphism 
, such that the compositions 
.
[edit] Examples
- In the category of abelian groups, the group of integers
is a generator: If f and g are different, then there is an element 
, such that 
. Hence the map 
, 
suffices. - Similarly, the one-point set is a generator for the category of sets.
