Discrete Conduche Fibrations and C*-algebras

TL;DR

This paper generalizes the concept of higher rank graphs as discrete Conduche fibrations to broader categories satisfying certain finiteness and lifting conditions, expanding the theoretical framework for C*-algebras.

Contribution

It introduces a generalized construction of discrete Conduche fibrations with finiteness and lifting properties over categories with specific conditions, extending previous graph-based models.

Findings

Generalization of higher rank graphs to broader categories

Establishment of conditions for fibrations with finiteness and lifting properties

Potential applications to C*-algebra theory

Abstract

The higher rank graphs of Kumjian and Pask are discrete Conduche fibrations over the monoid of k-tuples of natural numbers for some k in which every morphism in the base has a finite preimage under the the fibration. We examine the generalization of this construction to discrete Conduche fibrations with the same finiteness condition and a lifting property for completions of cospans to commutative squares, over any category satisfying a strong version of the right Ore condition, including all categories with pullbacks and right Ore categories in which all morphisms are monic.