Sjoerd Visscher<p>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.</p><p>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.</p><p>If you specialize to the proarrow equipment of functors and profunctors and simplify, you get the final expression. And if you then make S and T constant functors, and A and B monoidal actions, you get back mixed optics.</p><p><a href="https://types.pl/tags/categorytheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>categorytheory</span></a> <a href="https://types.pl/tags/optics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>optics</span></a></p>