Enriched Fell Bundles and Spaceoids

TL;DR

This paper introduces a new enriched categorical framework for Fell bundles, aiming to formalize spectral data in commutative C*-categories, potentially unifying various existing approaches.

Contribution

It defines involutive categorical bundles enriched in involutive monoidal categories, providing a novel setting for spectral data formalization in C*-categories.

Findings

Proposes a new definition of enriched Fell bundles.

Suggests this framework as suitable for spectral data formalization.

Lays groundwork for unifying spectral approaches in C*-categories.

Abstract

We propose a definition of involutive categorical bundle (Fell bundle) enriched in an involutive monoidal category and we argue that such a structure is a possible suitable environment for the formalization of different equivalent versions of spectral data for commutative C*-categories.