Generator

Generator may refer to:

Mathematics

Computing

Generator (category theory)

In category theory in mathematics a family of generators (or family of separators) of a category is a collection of objects, indexed by some set I, such that for any two morphisms in , if then there is some i∈I and morphism , such that the compositions . If the family consists of a single object G, we say it is a generator (or separator).

Generators are central to the definition of Grothendieck categories.

The dual concept is called a cogenerator or coseparator.

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.

References

Generator (Foo Fighters song)

"Generator" is a Foo Fighters song, released as a single in 2000 from their third album There Is Nothing Left to Lose. The single was only released in Australia and also released as a limited edition single in Europe.

The song is particularly unique among the band's work because of Dave Grohl's implementation of the talk box in parts of the song. The usage of the device was partly inspired by Grohl's admiration of Peter Frampton and Joe Walsh, both of whom helped popularize it in the 1970s.

Track listing

Australian CD

(The EP also contains an enhanced segment containing exclusive documentary footage and photos)

European CD

(This version was available for only 1 week between March 6 and March 12, 2000, each CD was a limited, numbered edition and at the end of the week of release all remaining stock was deleted. As well as the music tracks it also included a multimedia 'enhanced' segment containing exclusive documentary footage and photos)