# direct product

Definition from Wiktionary, the free dictionary

## English[edit]

### Noun[edit]

**direct product** (*plural* **direct products**)

- (set theory) The set of functions from the indexing set of an indexed family of sets to the union of the family, whose values at any given index lie in the set indexed thereby.
- For example, if A and B are sets, their direct product is the set of pairs (a,b) with a in A and b in B.

- (mathematics) The generalization of
**direct product**(1) to arbitrary categories.

#### Translations[edit]

in set theory —

*see*Cartesian productin category theory —

*see*categorical product