nLab
product category

Contents

Contents

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.

Last revised on June 1, 2016 at 07:57:39. See the history of this page for a list of all contributions to it.