categorical product

English - English

Definition of categorical product in English English dictionary

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.

Hyphenation

cat·e·go·ri·cal prod·uct

Turkish pronunciation

kätıgôrîkıl prädıkt

Pronunciation

/ˌkatəˈgôrəkəl ˈprädəkt/ /ˌkætəˈɡɔːrɪkəl ˈprɑːdəkt/