Rocky Mountain Journal of Mathematics

Discrete Conduché fibrations and $C^*$-algebras

Jonathan H. Brown and David N. Yetter

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Abstract

The $k$-graphs in the sense of Kumjian and Pask~\cite {KP} are discrete Conduch\'{e} fibrations over the monoid~$\mathbb {N}^k$, satisfying a finiteness condition. We examine the generalization of this construction to discrete Conduch\'{e} 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.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 3 (2017), 711-756.

Dates
First available in Project Euclid: 24 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1498269809

Digital Object Identifier
doi:10.1216/RMJ-2017-47-3-711

Mathematical Reviews number (MathSciNet)
MR3682147

Zentralblatt MATH identifier
1369.18003

Subjects
Primary: 18D30: Fibered categories 22A22: Topological groupoids (including differentiable and Lie groupoids) [See also 58H05] 46L05: General theory of $C^*$-algebras

Keywords
Conduché fibrations Cuntz-Krieger algebra groupoids

Citation

Brown, Jonathan H.; Yetter, David N. Discrete Conduché fibrations and $C^*$-algebras. Rocky Mountain J. Math. 47 (2017), no. 3, 711--756. doi:10.1216/RMJ-2017-47-3-711. https://projecteuclid.org/euclid.rmjm/1498269809


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