|
|
Definition of Categorical product
1. Noun. (context: category theory) Given two objects ''X''1 and ''X''2, their '''product''' is an object ''X''1 × ''X''2, with projections π1 : ''X''1 × ''X''2 → ''X''1 and π2 : ''X''1 × ''X''2 → ''X''2, which satisfies the following ''universal property'': for any object ''Y'' with morphisms ''f''1 : ''Y'' → ''X''1 and ''f''2 : ''Y'' → ''X''2, there can naturally be constructed a unique morphism ''f'' : ''Y'' → ''X''1 × ''X''2 such that and . ¹
2. Noun. (context: category theory) The product generalizes, through associativity, to between more than two objects. ¹
¹ Source: wiktionary.com
Lexicographical Neighbors of Categorical Product
Other Resources:
