Lenses, fibrations and universal translations

Authors:
Michael Johnson;Robert Rosebrugh;R. J. Wood
Affiliations:
School of mathematics and computing, macquarie university, sydney, new south wales, australia email: michael.johnson@mq.edu.au;Department of mathematics and computer science, mount allison university, sackville, new brunswick, canada email: rrosebrugh@mta.ca;Department of mathematics and statistics, dalhousie university, halifax, nova scotia, canada email: rjwood@mathstat.dal.ca
Venue:
Mathematical Structures in Computer Science
Year:
2012

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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.