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Lenses, fibrations and universal translations†

Published online by Cambridge University Press:  19 September 2011

MICHAEL JOHNSON ,
ROBERT ROSEBRUGH  and
R. J. WOOD
MICHAEL JOHNSON
Affiliation:
School of Mathematics and Computing, Macquarie University, Sydney, New South Wales, Australia Email: Michael.Johnson@mq.edu.au
ROBERT ROSEBRUGH
Affiliation:
Department of Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick, Canada Email: rrosebrugh@mta.ca
R. J. WOOD
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada Email: rjwood@mathstat.dal.ca
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Abstract

This paper extends the ‘lens’ concept for view updating in Computer Science beyond the categories of sets and ordered sets. It is first shown that a constant complement view updating strategy also corresponds to a lens for a categorical database model. A variation on the lens concept called a c-lens is introduced, and shown to correspond to the categorical notion of Grothendieck opfibration. This variant guarantees a universal solution to the view update problem for functorial update processes.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 22 , Issue 1 , February 2012 , pp. 25 - 42
Copyright
Copyright © Cambridge University Press 2011

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