categorical product

Английский Язык - Английский Язык

Определение categorical product в Английский Язык Английский Язык словарь: The product generalizes, through associativity, to between more than two objects; Given two objects A and B, their product is an object A \times B , with projections \pi_1: A \times B \rightarrow A and \pi_2: A \times B \rightarrow B, which satisfies the following universal property: for any object X with arrows f: X\rightarrow A and g: X\rightarrow B, then there can naturally be constructed an arrow \langle f,g\rangle: X\rightarrow A \times B such that \pi_1 \circ \langle f,g\rangle = f and \pi_2 \circ \langle f,g\rangle = g, and this arrow is unique (in satisfying these two equations)
For the category of the poset of the natural numbers, in which arrows denote the relation less than or equal to, the categorical product is the greatest common denominator.

categorical product