We explore a curious type of equivalence between certain pairs of reflective and coreflective subcategories. We illustrate with examples involving noncommutative duality for $C^*$-dynamical systems and compact quantum groups, as well as examples where the subcategories are actually isomorphic.
Keywords: adjoint functors, reflective and coreflective subcategories, equivalent categories, $C^*$-algebras, coactions, quantum groups
2000 MSC: Primary 18A40; Secondary 46L55, 46L89
Theory and Applications of Categories, Vol. 25, 2011, No. 6, pp 142-179.
Published 2011-03-10.
http://www.tac.mta.ca/tac/volumes/25/6/25-06.dvi
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http://www.tac.mta.ca/tac/volumes/25/6/25-06.pdf
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ftp://ftp.tac.mta.ca/pub/tac/html/volumes/25/6/25-06.ps
Revised 2011-06-08. Original version at
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