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Isn't it amazing that these are all different representations of the same thing, each useful in its own way?
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I believe proarrow equipments are a great setting to study optics in. You can see the expression for optics and the equivalent string diagram below.
The string diagram even looks like it's just a schematic drawing of an optic, but it really contains all the required information! The arrow heads indicate that s, t, a and b are all tight arrows, but in the loose direction.
If you specialize to the p
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(comult @(D '["Y"]) == line || counit)
|| (comult @(D '["X"]) == mappend @(D '["X"]))
|| (comult @(D '["Z"]) == counit @(D '["Z"]) || line)
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line || unitAdj @"L" @"R" == counitAdj @"L" @"R" || line
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Isn't it amazing that these are all different representations of the same thing, each useful in its own way?
trace @_ @(D '["A"]) @(D '["X"]) @(D '["Y"]) (node "f" == node @'["Z"] "g")
line || unitAdj @"L" @"R" == counitAdj @"L" @"R" || line
(comult @(D '["Y"]) == line || counit)
|| (comult @(D '["X"]) == mappend @(D '["X"]))
|| (comult @(D '["Z"]) == counit @(D '["Z"]) || line)
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@mc Do you think dependent optics might fit in this framework?
You could even see the above string diagram as a comb. Chad Nester et al. figured this out for the free cornering in https://arxiv.org/pdf/2205.00842 but it works for any proarrow equipment!
I believe proarrow equipments are a great setting to study optics in. You can see the expression for optics and the equivalent string diagram below.
The string diagram even looks like it's just a schematic drawing of an optic, but it reall…
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