Category of metric spaces with continuous maps

This article describes a category (in the mathematical sense) whose objects are metric spaces. In other words, it gives a category structure to the collection of all metric spaces.
View other category structures on metric spaces

Definition

The category of metric spaces with continuous maps is defined as follows:

• The objects of this category are metric spaces.
• The morphisms of this category are continuous maps of metric spaces.

Related categories

• Category of topological spaces with continuous maps: In fact, we have a forgetful functor from the category of metric spaces with continuous maps to the category of topological spaces with continuous maps.
• Category of metric spaces with uniformly continuous maps: This is a subcategory with the same objects and fewer morphisms.
• Category of metric spaces with short maps: This is a subcategory with the same objects and fewer morphisms.