Geodesic
The Category of Ordered Bratteli Diagrams
Canadian journal of mathematics, Tome 73 (2021) no. 1, pp. 1-28

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DOI

A category structure for ordered Bratteli diagrams is proposed in which isomorphism coincides with the notion of equivalence of Herman, Putnam, and Skau. It is shown that the natural one-to-one correspondence between the category of Cantor minimal systems and the category of simple properly ordered Bratteli diagrams is in fact an equivalence of categories. This gives a Bratteli–Vershik model for factor maps between Cantor minimal systems. We give a construction of factor maps between Cantor minimal systems in terms of suitable maps (called premorphisms) between the corresponding ordered Bratteli diagrams, and we show that every factor map between two Cantor minimal systems is obtained in this way. Moreover, solving a natural question, we are able to characterize Glasner and Weiss’s notion of weak orbit equivalence of Cantor minimal systems in terms of the corresponding C*-algebra crossed products.
DOI : 10.4153/S0008414X19000452
Mots-clés : Cantor minimal system, ordered Bratteli diagram, premorphism, category, functor, C*-algebra, dimension group, weak orbit equivalence 
Amini, Massoud; Elliott, George A.; Golestani, Nasser. The Category of Ordered Bratteli Diagrams. Canadian journal of mathematics, Tome 73 (2021) no. 1, pp. 1-28. doi: 10.4153/S0008414X19000452
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