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• CommentRowNumber1.
• CommentAuthorDavid_Corfield
• CommentTimeSep 24th 2018

There’s a first stab at it.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeSep 24th 2018

Judging by Prop 3.1 of Lenses, fibrations and universal translations, lenses are just algebras for our possibility monad, at necessity and possibility.

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeSep 24th 2018

It seems the terminology isn’t fixed, so I added a noted about ’well-behaved’ lenses.

• CommentRowNumber4.
• CommentAuthorspitters
• CommentTimeSep 24th 2018

I’m told this is good. But I don’t have access at the moment: https://dl.acm.org/citation.cfm?doid=3191697.3191718

Lenses for philosophers

and of course we should cite the paper by Mitchell that started the discussion.

• CommentRowNumber5.
• CommentAuthorDavid_Corfield
• CommentTimeSep 24th 2018
• (edited Sep 24th 2018)

Given

necessity comonad : possibility monad = jet comonad : infinitesimal disk bundle monad,

and since lens (in computer science) (at least lawlike ones) seem to be algebras for the possibility monad, what are algebras for the infinitesimal disk bundle?

We’d need, $E$ over $X$ and a map $T_{inf} X \times_X E \to E/X$.

• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeSep 24th 2018

Oh, is it just the constants $E = K \times X$. But then what’s that exciting about lenses?

That paper Lenses, fibrations and universal translations continues that when the $V$ of views is such that $V \to 1$ is split epi then a lens just is a projection.

So people look at more general situations?

1. Optic_C

Ammar Husain

• CommentRowNumber8.
• CommentAuthorDavid_Corfield
• CommentTimeJan 23rd 2020

Added a reference to a talk.

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