In category theory, the domain of a morphism is its source
object; that is, the domain of f:XYf\colon X \to Y is XX. In
particular, this is the case for a function: its domain is the
set of elements to which it can be applied.  However, this can
conflict with other meanings of ‘domain’, especially in a
category like Rel. For instance, for any subset AXA\subseteq X,
there exists a relation R:XYR\colon X \to Y whose “domain” is AA
under some uses of the term.  Other similar meanings of the term
include:  A separate meaning of ‘domain’ occurs in domain
theory, which is at the interface of logic and theoretical
computer science. There a domain is a particular type of poset.
Revised on July 8, 2013 10:25:01 by Urs Schreiber (