Adjoints, wrapping, and morphisms at infinity

For a localization of a smooth proper category along a subcategory preserved by the Serre functor, we show that morphisms in Efimov’s algebraizable categorical formal punctured neighborhood of infinity can be computed using the natural cone between right and left adjoints of the localization functor. In particular, this recovers the following result of Ganatra–Gao–Venkatesh: morphisms in categorical formal punctured neighborhoods of wrapped Fukaya categories are computed by Rabinowitz wrapping.