Categories with norms

Abstract

We study a metric-like structure on categories, showing that the concept of the limit of a sequence in a metric space and the concept of the colimit of a sequence in a category have a common generalization. The main concept is a norm on a category, generalizing pseudo-metrics and group valuations. In this new context, we discuss topics like Cauchy completion and the Banach Contraction Principle.

20 pages

References in corpus (2)

• Banach spaces of universal disposition
• Categories, norms and weights

Cited by in corpus (1)

• Categorical Structures on Bundle Gerbes and Higher Geometric Prequantisation