Lenses and their generalisations: a guide to the design space

Jules Hedges (University and College Union)

22-Feb-2022, 17:00-18:00 (2 years ago)

Abstract: The number of variants of lens-like structures, plus some questionable terminology, can seem overwhelming. I will tour some of the main variants, with emphasis on exactly what conditions on the base category are necessary for the construction, and how they relate to each other. We will visit: (1) lenses over a cartesian category, (2) linear lenses over a monoidal closed category, (3) optics over a monoidal category, or more generally a pair of actegories, (4) dependent lenses over a category with pullbacks, or more generally an indexed category, and (5) polynomial natural transformations over a locally cartesian closed category. Unifying these motivates the problem of “dependent optics”, which will be the topic of several future seminars.

I am on strike action during this talk and I represent myself as an independent researcher, not my employer. I will use some of my time to discuss this. More information about our grievances can be found here: www.ucu.org.uk/article/11896/Why-were-taking-action

category theory

Audience: researchers in the topic

( video )


Intercats: Seminar on Categorical Interaction

Organizer: Toby St Clere Smithe*
*contact for this listing

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