nLab
product category

Definition

For CC and DD two categories, the product category C×DC \times D is the category whose

  • objects are ordered pairs (c,d)(c,d) with cc an object of CC and dd an object of DD;

  • morphisms are ordered pairs ((cfc),(dgd))((c \stackrel{f}{\to} c'),(d \stackrel{g}{\to} d')),

  • composition of morphisms is defined componentwise by composition in CC and DD.

This operation is the cartesian product in the 1-category Cat.

Revised on August 19, 2013 12:01:13 by Anonymous Coward (75.82.75.149)