Adjoints, wrapping, and morphisms at infinity

TL;DR

This paper provides a method to compute morphisms in certain localized categories using adjoints, connecting formal neighborhoods at infinity with wrapped Fukaya categories and Rabinowitz wrapping.

Contribution

It introduces a new approach to compute morphisms in algebraizable categorical formal neighborhoods via adjoints, unifying concepts in symplectic geometry and category theory.

Findings

Morphisms in formal neighborhoods can be computed using cones between adjoints.

The method recovers known results in wrapped Fukaya categories.

Provides a conceptual framework linking formal neighborhoods and Rabinowitz wrapping.

Abstract

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.