Revision as of 08:59, 1 January 2008 by imported>Giovanni Antonio DiMatteo
Category theory
Definition
A category consists of the following data:
- A class of "objects," denoted

- For objects
, a set
such that
is empty if
and 
together with a "law of composition":
(which we denote by
) having the following properties:
- Associativity:
whenever the compositions are defined
- Identity: for every object
there is an element
such that for all
,
and
.
Examples
- The category of sets:
- The category of topological spaces:
- The category of functors: if
and
are two
categories, then there is a category consisting of all contravarient functors from
to
, where morphisms are natural transformations.
- The category of schemes is one of the principal objects of study