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.
Citation
Jonathan H. Brown. David N. Yetter. "Discrete Conduché fibrations and $C^*$-algebras." Rocky Mountain J. Math. 47 (3) 711 - 756, 2017. https://doi.org/10.1216/RMJ-2017-47-3-711
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