Rocky Mountain Journal of Mathematics

Discrete Conduché fibrations and $C^*$-algebras

Jonathan H. Brown and David N. Yetter

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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.

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

First available in Project Euclid: 24 June 2017

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Zentralblatt MATH identifier

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

Conduché fibrations Cuntz-Krieger algebra groupoids


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.

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