## Fibrations and universal translations

### Bob Rosebrugh – 18 August 2010

Solving the "view update problem" for database updates interpreted as processes requires what have been called "translations". From this perspective, the view update problem can be seen as a lifting problem. Thus it is not surprising that fibrations play a role.

We have studied view definitions with "lens" structure, They are essentially projections and do provide translations. When C = Cat a lens G:S-->V is an opfibration. On the other hand, taking the projection (G,1_V) --> V from the comma category is the functor part of a monad on Cat/V. An algebra for (-,1_V) (an opfibration) provides a good notion of a generalized lens. Furthermore, an opfibration has "universal translations". These provide a universal solution to the view updating problem when G = W*:Mod(E) --> Mod(V) for a view (sketch morphism) W:V-->E in the Sketch Data Model.

Joint work with Mike Johnson and Richard Wood.

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