Geodesic
The Category of Bratteli Diagrams
Canadian journal of mathematics, Tome 67 (2015) no. 5, pp. 990-1023

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DOI

A category structure for Bratteli diagrams is proposed and a functor from the category of $\text{AF}$ algebras to the category of Bratteli diagrams is constructed. Since isomorphism of Bratteli diagrams in this category coincides with Bratteli’s notion of equivalence, we obtain in particular a functorial formulation of Bratteli’s classification of $\text{AF}$ algebras (and at the same time, of Glimm’s classification of $\text{UHF}$ algebras). It is shown that the three approaches to classification of $\text{AF}$ algebras, namely, through Bratteli diagrams, $\text{K}$ -theory, and a certain natural abstract classifying category, are essentially the same from a categorical point of view.
DOI : 10.4153/CJM-2015-001-8
Mots-clés : 46L05, 46L35, 46M15, C*-algebra, category, functor, AF algebra, dimension group, Bratteli diagram 
Amini, Massoud; Elliott, George A.; Golestani, Nasser. The Category of Bratteli Diagrams. Canadian journal of mathematics, Tome 67 (2015) no. 5, pp. 990-1023. doi: 10.4153/CJM-2015-001-8
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     title = {The {Category} of {Bratteli} {Diagrams}},
     journal = {Canadian journal of mathematics},
     pages = {990--1023},
     year = {2015},
     volume = {67},
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     doi = {10.4153/CJM-2015-001-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-001-8/}
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