product-preserving function
nounUK /ˈprɒdʌkt prɪˈzɜːvɪŋ ˈfʌŋkʃən/
US /ˈprɑːdʌkt prɪˈzɜːrvɪŋ ˈfʌŋkʃən/
A product-preserving function is a rule that keeps things combined in the same way when you move them to a new place.
In category theory, a functor that maps products to products is called a product-preserving function.
SYNONYMS
OTHER MEANINGS
2. In algebra, a function between structures that respects the multiplication operation, so f(a·b) = f(a)·f(b).
The logarithm is a product-preserving function because log(xy) = log(x) + log(y).
3. A mapping that sends a Cartesian product to a Cartesian product componentwise.
The coordinate swap is a product-preserving function on ordered pairs.
4. A function that commutes with the formation of direct products of groups or rings.
The projection map is product-preserving when applied to direct products of groups.