category theory

# Contents

## Meanings

In category theory, the domain of a morphism is its source object; that is, the domain of $f\colon X \to Y$ is $X$. 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 $A\subseteq X$, there exists a relation $R\colon X \to Y$ whose “domain” is $A$ 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 (89.204.135.61)