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@CAT Seminar

Presented by : Bob Rosebrugh (Mount Allison)

Topic : Universal updates for symmetric lenses

Abstract: "Asymmetric" lenses provide a strategy to lift updates in a model domain along a morphism of model domains. A "symmetric" lens between two model domains has state synchronization data and resynchronization operations. When the model domains are categories we speak of delta-lenses (or d-lenses).In previous work we showed that (certain equivalence classes of) spans of asymmetric d-lenses represent symmetric d-lenses. Asymmetric c-lenses are a special case of asymmetric d-lenses whose updates satisfy a universal property which can be construed as "least-change''. So it was natural to hope that symmetric c-lenses characterize the symmetric d-lenses which satisfy a natural universal property.

Instead, we'll explain why we do not expect all symmetric c-lenses (viewed as equivalence classes of spans of c-lenses) to be central to developing universal properties for symmetric d-lenses. We consider instead cospans of c-lenses and show that they generate symmetric c-lenses with a universal property. That property is further analyzed towards obtaining universal, least-change, properties for symmetric d-lenses. We also explore how to characterize those symmetric d-lenses that arise from cospans of c-lenses.  (Joint work with Michael Johnson) 


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Colloquium Room #319 Chase Building