Homotopic distance between functors

TL;DR

This paper introduces a new concept of homotopic distance between functors in category theory, extending previous work on categorical LS-category and adapting topological homotopic ideas to small categories.

Contribution

It defines the categorical homotopic distance between functors, generalizing the categorical LS-category and bridging topological homotopy concepts with category theory.

Findings

Defines categorical homotopic distance between functors.

Generalizes the categorical LS-category.

Provides a new framework linking topology and category theory.

Abstract

We introduce a notion of categorical homotopic distance between functors by adapting the notion of homotopic distance in topological spaces, recently defined by the authors to the context of small categories. Moreover, this notion generalizes the work on categorical LS-category of small categories by Tanaka.