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This paper constructs and studies the Rabinowitz (wrapped) Fukaya category, acategorical invariant of exact cylindrical Lagrangians in a Liouville manifoldwhose cohomological morphisms, ``Rabinowitz wrapped Floer homology groups"measure the failure of wrapped Floer cohomology to satisfy Poincare duality(and in particular vanish for any pair with at least one compact Lagrangian).Our main result, answering a conjecture of Abouzaid, relates the Rabinowitz andusual wrapped Fukaya category by way of a general construction introduced byEfimov, the categorical formal punctured neighborhood of infinity. As anapplication, we show how Rabinowitz Fukaya categories can be fit into - and inparticular often computed in terms of - mirror symmetry.

Rabinowitz Fukaya categories and the categorical formal punctured neighborhood of infinity