Generator (category theory)

From formulasearchengine
Jump to navigation Jump to search

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.

Generators are central to the definition of Grothendieck categories.

The dual concept is called a cogenerator or coseparator.



  • {{#invoke:citation/CS1|citation

|CitationClass=citation }}, p. 123, section V.7

External links