Editing Category of metric spaces (section)

{{Short description|Category whose objects are metric spaces and whose morphisms are metric maps}}
In [[category theory]], '''Met''' is a [[Category (mathematics)|category]] that has [[metric space]]s as its [[object (category theory)|objects]] and [[metric map]]s ([[Continuous_function#Continuous_functions_between_metric_spaces|continuous]] [[Function (mathematics)|functions]] between metric spaces that do not increase any pairwise distance) as its [[morphism]]s. This is a category because the [[Function composition|composition]] of two metric maps is again a metric map. It was first considered by {{harvtxt|Isbell|1964}}.