 Product order

In mathematics, given two ordered sets A and B, one can induce a partial ordering on the Cartesian product A × B. Given two pairs (a_{1},b_{1}) and (a_{2},b_{2}) in A × B, one sets
 (a_{1},b_{1}) ≤ (a_{2},b_{2})
if and only if a_{1} ≤ a_{2} and b_{1} ≤ b_{2}.
This ordering is called the product order. Another possible ordering on A × B is the lexicographical order.
The Cartesian product with product order is the categorical product in the category of partially ordered sets with monotone functions.
See also
 direct product of binary relations
 examples of partial orders
 orders on the Cartesian product of totally ordered sets
Categories: Mathematics stubs
 Order theory
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