In category theory, the domain of a morphism is generally the same as its source; that is, the domain of is . 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 , there exists a relation whose “domain” is 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 August 13, 2012 22:11:29
by Mike Shulman