A characterization of representable intervals

TL;DR

This paper characterizes representable intervals in symmetric monoidal closed categories, linking algebraic structures to the formation of finitely bicomplete 2-categories and exploring their connections with homotopy theory.

Contribution

It provides a new algebraic characterization of representable intervals that induce 2-category structures, with examples and links to homotopy theory.

Findings

Characterization of representable intervals via algebraic structure

Examples illustrating the theory

Connections with homotopy theory of 2-categories

Abstract

In this note we provide a characterization, in terms of additional algebraic structure, of those intervals (certain cocategory objects) in a symmetric monoidal closed category E that are representable in the sense of inducing on E the structure of a finitely bicomplete 2-category. Several examples and connections with the homotopy theory of 2-categories are also discussed.