Double Fibrations

TL;DR

This paper introduces the concept of double fibrations in double categories, explores their key properties and examples, and establishes their relation to existing fibrational notions, including a representation theorem.

Contribution

It defines double fibrations, relates them to known fibrations, and proves a representation theorem, advancing the theoretical understanding of fibrations in double categories.

Findings

Double fibrations are characterized as a new class of fibrations in double categories.

They relate to monoidal and discrete double fibrations, unifying existing concepts.

A representation theorem for double fibrations is established.

Abstract

This paper defines double fibrations (fibrations of double categories) and describes their key examples and properties. In particular, it shows how double fibrations relate to existing fibrational notions such as monoidal fibrations and discrete double fibrations, proves a representation theorem for double fibrations, and shows how double fibrations are a type of internal fibration.